Linear Function Calculator (Find y = mx + b from Two Points or a Slope and a Point, Rate of Change and Intercepts)

Choose a mode and enter the coordinates of two points (or the slope and the coordinates of one point). If you also enter an x, the value of y for that x is calculated too.

Find the line from

Point 1 x-coordinate x1

Point 1 y-coordinate y1

Point 2 x-coordinate x2

Point 2 y-coordinate y2

Slope m (rate of change)

x to find y for (optional)

Decimals, negative numbers and fractions such as 3/4 can be used. The fields you do not need switch automatically with the mode.

Result and graph

Enter the coordinates (or the slope) in the fields on the left and press "Calculate". The result and a graph will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formulas and graphs
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Find the equation $y = mx + b$ of the line through two points $(x_1,\ y_1)$ and $(x_2,\ y_2)$ on the spot, just by entering the coordinates
You can also choose a mode that finds the equation from the slope $m$ and one point on the line
The slope (rate of change) is shown with the steps of $m = \dfrac{\Delta y}{\Delta x}$. Answers are shown as fractions in lowest terms (exact values)
It also finds where the line crosses the x-axis and the y-axis and the value of $y$ for an $x$ you choose, and draws a graph of the line
If the two points have the same x-coordinate, so the line is not a linear function, it tells you that the line is the vertical line "x = constant" and explains why
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

Coordinates and slopes can be decimals, negative numbers or fractions such as 3/4.

What is this calculation used for?

Predicting costs on a pricing plan (phone, electricity, taxi)

A price made of "a base fee plus a charge for each unit you use" is exactly the linear function $y = mx + b$: the y-intercept $b$ is the base fee and the slope $m$ is the price per unit. For example, a taxi that charges $3.50 to start plus $2.50 per mile costs $y = 2.5x + 3.5$, so a 4-mile ride costs $2.5 \times 4 + 3.5 = 13.50$ dollars.
Working out the unit price and the base fee from two monthly bills (two points of usage and amount) is exactly "finding the equation from two points".

Understanding how a spring stretches (science, Hooke's law)

A spring stretches in proportion to the weight hung on it (Hooke's law), so the total length of the spring, "natural length + stretch", is a linear function. For example, a spring with a natural length of 10 cm that stretches 2 cm for each weight has length $y = 2x + 10$ ($x$ is the number of weights).
If you fix the equation from two measurements in an experiment (two points), you can predict the length for weights you have not tried yet. It is a classic example that links middle school science and math.

Estimating the temperature from the altitude (hiking and weather)

As a rough average, air gets about 3.5°F cooler for every 1,000 ft you climb (this is called the lapse rate). If you know the temperature at the bottom, a linear function gives a rough estimate of the temperature at the top. For example, if it is 77°F at the trailhead, the temperature at $x$ thousand feet higher is about $y = 77 - 3.5x$, so at a summit 6,000 ft higher it is about 56°F.
The real temperature also depends on the weather and humidity, so this is not an exact formula, but it is a practical approximation for deciding what to wear on a hike.

Predicting sales and costs (business, break-even)

Business costs often take the form "fixed costs such as rent + a variable cost for each item made", which is also a linear function: the y-intercept is the fixed cost and the slope is the variable cost per item.
Comparing the cost line with the sales line shows "how many you need to sell to make a profit" (the break-even point). It is a widely used first step in a business plan.

Converting temperature units (Celsius and Fahrenheit)

Fahrenheit (°F), used in the US, and Celsius (°C), used in most other countries, are related exactly by the linear function $F = 1.8C + 32$. With slope 1.8 and y-intercept 32, it is a familiar example of an exactly linear relationship.
For example, 20°C is $1.8 \times 20 + 32 = 68$ °F. You can use this formula directly to read a weather forecast abroad or an oven temperature in a recipe from another country.

Formulas and graphs

Equation of a linear function $y = mx + b$ (slope-intercept form)

Graph

Standard notation (the usual math form)

$y$ $=$ $m$ $\times$ $x$ $+$ $b$

In words (symbols replaced with words)

④ y-coordinate of a point on the line $y$ $=$ ② slope $m$ (rate of change) $\times$ ① x-coordinate $x$ $+$ ③ y-intercept $b$

The formula in words

① Take the x-coordinate $x$

② multiply it by the slope $m$ (how much y increases each time x increases by 1)

③ add the y-intercept $b$ (the value of y when x = 0)

④ and you get the y-coordinate of the point on the line $y$

Quick example

For the linear function $y = 2x + 1$, with slope 2 and y-intercept 1, the value of $y$ when $x = 3$ is

y-coordinate $y$ $=$ slope (2) $\times$ x-coordinate (3) $+$ y-intercept (1)

$y = 2 \times 3 + 1 = 7$

Key idea

A linear function is a function of the form $y = mx + b$, and its graph is a straight line. The word "linear" tells you that $x$ appears only to the first power (no $x^2$ or $x^3$). The slope $m$ tells you "how much y changes each time x increases by 1", and the y-intercept $b$ is "the starting height (y when x = 0)". For example, a pricing plan of "a base fee of $b$ dollars plus a rate of $m$ dollars for each unit $x$ you use" has exactly this form. Direct variation $y = kx$, taught in Grade 7, is the special linear function whose y-intercept is 0 (its line passes through the origin).

Finding the slope $m$ (rate of change) from two points

Graph

Standard notation (the usual math form)

$m$ $=$ $y_2 - y_1$ $\div$ $x_2 - x_1$

In words (symbols replaced with words)

③ slope $m$ (rate of change) $=$ ① change in y (rise) $\Delta y = y_2 - y_1$ $\div$ ② change in x (run) $\Delta x = x_2 - x_1$

The formula in words

① Take the change in y, $\Delta y$ (how far it went up or down)

② divide it by the change in x, $\Delta x$ (how far it went across)

③ and you get the slope $m$ (rate of change)

Quick example

The slope (rate of change) of the line through the two points (1, 3) and (4, 9) is

slope $m$ $=$ change in y (9 − 3 = 6) $\div$ change in x (4 − 1 = 3)

$m = \dfrac{9 - 3}{4 - 1} = \dfrac{6}{3} = 2$

Key idea

The rate of change, taught with linear functions in Grade 8, is $\dfrac{\text{change in } y}{\text{change in } x}$, often called "rise over run". For a linear function this value is the same wherever you measure it, and it is exactly the slope $m$ (for a curve, it depends on where you measure). Subtract in the same order on the top and the bottom. If you subtract point 1 from point 2, do it in that order in both. If you mix the order, the sign comes out reversed. When the two points have the same x-coordinate ($\Delta x = 0$), you would be dividing by 0, so the slope is undefined. The line through the two points is then a vertical line parallel to the y-axis, "x = constant", which is not the graph of a linear function (this calculator detects this case and explains it).

Finding the y-intercept $b$ from the slope and one point

Standard notation (the usual math form)

$b$ $=$ $y_1$ $-$ $m$ $\times$ $x_1$

In words (symbols replaced with words)

④ y-intercept $b$ $=$ ③ y-coordinate of the point $y_1$ $-$ ① slope $m$ $\times$ ② x-coordinate of the point $x_1$

The formula in words

① Multiply the slope $m$

② by the x-coordinate of the point $x_1$ (this is how much y grows on the way from x = 0 to the point)

③ and subtract it from the y-coordinate of the point $y_1$

④ to get the y-intercept $b$

Quick example

The y-intercept of the line with slope 2 through the point (3, 7) is

y-intercept $b$ $=$ y-coordinate (7) $-$ slope (2) $\times$ x-coordinate (3)

$b = 7 - 2 \times 3 = 1$

$y = 2x + 1$

Key idea

Saying that the point $(x_1,\ y_1)$ is on the line tells you that substituting it into the equation, $y_1 = m x_1 + b$, is true. Solving this for $b$ gives $b = y_1 - m x_1$. (This is the same as starting from point-slope form, $y - y_1 = m(x - x_1)$, and rewriting it in slope-intercept form.) When you find the equation from two points, you first find the slope $m$ as the rate of change, and then you only need to substitute either point into this formula. So in both modes, the last step comes down to this formula.

Where the line crosses the x-axis and the y-axis (the intercepts)

Graph

Standard notation (the usual math form)

$x$ $=$ $-$ $b$ $\div$ $m$

In words (symbols replaced with words)

③ x-intercept (where it crosses the x-axis) $=$ $-$ ① y-intercept $b$ $\div$ ② slope $m$

The formula in words

① Take the y-intercept $b$ with its sign reversed

② divide it by the slope $m$

③ and you get the x-intercept (where it crosses the x-axis) (it crosses the y-axis at $(0,\ b)$)

Quick example

To find where $y = 2x + 1$ crosses the x-axis, substitute $y = 0$:

x-intercept $=$ $-$ y-intercept (1) $\div$ slope (2)

$0 = 2x + 1$

$x = -\dfrac{1}{2}$

Key idea

The line crosses the x-axis "where $y = 0$", so solving $0 = mx + b$ for $x$ gives the x-intercept $x = -\dfrac{b}{m}$. This is an important way to see linear functions: the solution of the equation $mx + b = 0$ matches the point where the graph crosses the x-axis. The line crosses the y-axis "where $x = 0$", and substituting gives $y = b$. So the y-intercept $b$ is exactly "the height where the graph crosses the y-axis". When the slope is 0 (the horizontal line $y = b$), the line is parallel to the x-axis and never crosses it (if $b = 0$, the line is the x-axis itself).

To find the equation $y = mx + b$ of a line from two points, find the slope $m = \dfrac{\Delta y}{\Delta x}$ (the rate of change) first, then the y-intercept $b = y_1 - m x_1$. From the slope and one point, you only need the y-intercept. The y-intercept $b$ is the height where the line crosses the y-axis, and $-\dfrac{b}{m}$ is the x-coordinate where it crosses the x-axis.

Symbols and terms

Symbols

$y = mx + b$	y equals m x plus b	The slope-intercept form of a linear function: $m$ is the slope and $b$ is the y-intercept. This is the standard form in US schools. (Some countries write it $y = ax + b$.)
$m$	m	The slope (rate of change): how much y increases each time x increases by 1. Nobody knows for sure why the letter m is used for slope.
$b$	b	The y-intercept: the value of y when x = 0, which is the height where the graph crosses the y-axis.
$x_1,\ y_1$	x sub 1, y sub 1	The coordinates of point 1. The small number at the lower right is called a subscript; it is a label for "which point" (it is not multiplication or an exponent).
$\Delta$	delta	The capital Greek letter delta, the Greek D, as in "difference". It stands for "change". $\Delta x$ is the change in x and $\Delta y$ is the change in y.
$\left(-\dfrac{b}{m},\ 0\right)$	negative b over m, zero	The point where the line crosses the x-axis. Its y-coordinate is 0, and its x-coordinate is $-\dfrac{b}{m}$, the solution of the equation $mx + b = 0$.
$(0,\ b)$	zero, b	The point where the line crosses the y-axis. Its x-coordinate is 0, and its y-coordinate is the y-intercept $b$ itself.

Terms

linear function	A function of the form $y = mx + b$. Its graph is a straight line. The word "linear" tells you that x appears only to the first power. Taught in Grade 8.
function	A rule that gives back exactly one number for each number you put in. Think of it as a machine: put in $x$ and out comes $y$. For example, put 3 into the machine $y = 2x + 1$ and 7 comes out.
slope	A number that tells "how much the line goes up or down for every 1 it goes across" (rise over run). A positive slope rises from left to right, a negative slope falls, and a slope of 0 gives a horizontal line.
rate of change	The change in y divided by the change in x, $\dfrac{\Delta y}{\Delta x}$. For a linear function it is the same wherever you measure it, and it equals the slope $m$.
y-intercept	The y-coordinate of the point where the graph crosses the y-axis (the value of y when x = 0). In the linear function $y = mx + b$, it is $b$. (The x-intercept is where the graph crosses the x-axis.)
direct variation	A relationship of the form $y = kx$ (a proportional relationship). When x doubles or triples, y doubles or triples too. It is the special linear function whose y-intercept $b$ is 0 (its line passes through the origin). Taught in Grade 7.
coordinates	A pair of numbers $(x,\ y)$ that gives the position of a point. The horizontal position is the x-coordinate and the vertical position is the y-coordinate.
coordinate plane	A plane made by crossing a horizontal number line (the x-axis) and a vertical number line (the y-axis) at a right angle. It is the grid you draw graphs on.
origin	The point $(0,\ 0)$ where the x-axis and the y-axis cross. It is written $O$, from "origin".
crossing point	The point where two lines cross. On this page, you find the points where a line crosses the x-axis and the y-axis.
change in y	How much a value increased, found as "after − before" (the change in x is found the same way). If the value went down, the change is negative.
constant	A fixed number that does not change. In an equation such as "x = 2", the 2 is a constant, and the equation stands for the vertical line whose x-coordinate is always 2.
constant function	A function whose y-value is always the same, whatever x is. Its equation has the form $y = b$, and its graph is a horizontal line parallel to the x-axis. It is $y = mx + b$ with $m = 0$; some textbooks count it as a linear function and some do not.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
If you get stuck, going back over these topics is the quickest way forward.

Positive and negative numbers (Grades 6–7)	Being able to subtract with negative numbers (example: $3 - (-1) = 4$) Knowing the sign rules for multiplying and dividing negative and positive numbers (example: $(-3) \times 2 = -6$)
The coordinate plane (Grades 5–6)	Being able to write the position of a point as a pair $(x,\ y)$ (example: the point $(2,\ 3)$ is "2 to the right and 3 up") Knowing where the x-axis, the y-axis and the origin are
Proportional relationships (Grade 7)	Knowing that the graph of direct variation $y = kx$ is a line through the origin Knowing that the constant $k$ tells "how much y increases when x increases by 1"
Expressions and equations (Grades 6–8)	Being able to substitute numbers into an expression such as $y_1 = m x_1 + b$ Being able to solve a linear equation such as $0 = 2x - 6$ (used to find where the line crosses the x-axis)
Working with fractions (Grades 5–7)	Being able to simplify fractions such as $\dfrac{6}{3} = 2$ Being comfortable leaving answers as fractions (and able to turn $\dfrac{3}{2}$ into 1.5)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to find the equation of a line from two points

Point 1 x-coordinate x1	1
Point 1 y-coordinate y1	3
Point 2 x-coordinate x2	4
Point 2 y-coordinate y2	9
Slope m (rate of change)	=(B4-B2)/(B3-B1)
y-intercept b	=B2-B5*B1
x-intercept (x where it crosses the x-axis)	=-B6/B5

Table to find the equation of a line from the slope and one point

Slope m	2
x-coordinate of the point x1	3
y-coordinate of the point y1	7
y-intercept b	=B3-B1*B2
x to find y for	5
Value of y for that x	=B1*B5+B4

Table to find where the line crosses the x-axis and the y-axis

Slope m	2
y-intercept b	1
x-intercept (x where it crosses the x-axis)	=-B2/B1
y where it crosses the y-axis	=B2

After pasting, the upper rows (coordinates and slope) are your inputs and the lower rows are calculated automatically.
The first table finds the equation from the two points (1, 3) and (4, 9): the slope m is 2, the y-intercept b is 1 (the equation of the line is y = 2x + 1), and the x-intercept is −0.5. "/" is division and "*" is multiplication.
The second table works from the slope 2 and the point (3, 7): the y-intercept b is 1, and y is 11 when x = 5.
The third table finds only where the line crosses the axes, from its equation (slope and y-intercept). If the two points have the same x-coordinate, the divisor is 0 and an error (#DIV/0!) appears. This matches the fact that the slope is undefined (the line is not a linear function).

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to find the equation of a line from two points

Point 1 x-coordinate x1	1
Point 1 y-coordinate y1	3
Point 2 x-coordinate x2	4
Point 2 y-coordinate y2	9
Slope m (rate of change)	=(B4-B2)/(B3-B1)
y-intercept b	=B2-B5*B1
x-intercept (x where it crosses the x-axis)	=-B6/B5

Table to find the equation of a line from the slope and one point

Slope m	2
x-coordinate of the point x1	3
y-coordinate of the point y1	7
y-intercept b	=B3-B1*B2
x to find y for	5
Value of y for that x	=B1*B5+B4

Table to find where the line crosses the x-axis and the y-axis

Slope m	2
y-intercept b	1
x-intercept (x where it crosses the x-axis)	=-B2/B1
y where it crosses the y-axis	=B2

The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the coordinates and slope with your own numbers.

How to calculate it in Python

from fractions import Fraction

# Coordinates of the two points (a fraction such as 3/4 can be written Fraction(3, 4))
x1, y1 = Fraction(1), Fraction(3)
x2, y2 = Fraction(4), Fraction(9)

slope = (y2 - y1) / (x2 - x1)   # slope m (rate of change) = Δy ÷ Δx
intercept = y1 - slope * x1     # y-intercept b = y1 − m×x1

print(f"Slope m = {slope}")
print(f"y-intercept b = {intercept}")
print(f"Equation of the line: y = {slope}x + {intercept}")
if slope != 0:
    print(f"Crosses the x-axis at: ({-intercept / slope}, 0)")
print(f"Crosses the y-axis at: (0, {intercept})")

x_value = Fraction(5)           # the x to find y for
print(f"When x = {x_value}, y = {slope * x_value + intercept}")

With the fractions module from the standard library, you can calculate with exact fractions and no decimal rounding errors. This example finds the equation from the two points (1, 3) and (4, 9). Running it prints the slope 2 and the y-intercept 1 (y = 2x + 1), the x-axis crossing point (-1/2, 0), and y = 11 when x = 5. Change the coordinates and run it.

How to write it in LaTeX and other math languages (copy and paste)

Equation of a linear function $y = mx + b$ (slope-intercept form)

y = mx + b

y = mx + b

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>y</mi>
    <mo>=</mo>
    <mi>m</mi><mi>x</mi>
    <mo>+</mo>
    <mi>b</mi>
  </mrow>
</math>

y = m x + b

y == m x + b

y := m*x + b;

y = m*x + b;

y = mx + b

Finding the slope $m$ (rate of change) from two points

m = (y₂ − y₁) ÷ (x₂ − x₁)

m = \frac{y_2 - y_1}{x_2 - x_1}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mfrac>
      <mrow><msub><mi>y</mi><mn>2</mn></msub><mo>&#x2212;</mo><msub><mi>y</mi><mn>1</mn></msub></mrow>
      <mrow><msub><mi>x</mi><mn>2</mn></msub><mo>&#x2212;</mo><msub><mi>x</mi><mn>1</mn></msub></mrow>
    </mfrac>
  </mrow>
</math>

m = (y_2 - y_1)/(x_2 - x_1)

(y2 - y1)/(x2 - x1)

m := (y2 - y1)/(x2 - x1);

m = (y2 - y1)/(x2 - x1);

m = (y_2 - y_1)/(x_2 - x_1)

Finding the y-intercept $b$ from the slope and one point

b = y₁ − mx₁

b = y_1 - m x_1

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>b</mi>
    <mo>=</mo>
    <msub><mi>y</mi><mn>1</mn></msub>
    <mo>&#x2212;</mo>
    <mi>m</mi>
    <msub><mi>x</mi><mn>1</mn></msub>
  </mrow>
</math>

b = y_1 - m x_1

y1 - m x1

b := y1 - m*x1;

b = y1 - m*x1;

b = y_1 - m x_1

Where the line crosses the x-axis and the y-axis (the intercepts)

x = −b ÷ m

x = -\frac{b}{m}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>x</mi>
    <mo>=</mo>
    <mo>&#x2212;</mo>
    <mfrac><mi>b</mi><mi>m</mi></mfrac>
  </mrow>
</math>

x = -b/m

-b/m

x := -b/m;

x = -b/m;

x = −b/m

How to have ChatGPT do the calculation

You are a math calculation assistant for linear functions. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

Find the equation y = mx + b of the line through the two points (1, 3) and (4, 9).
Show each of the following:
1. The slope m (rate of change), with the steps of Δy/Δx
2. The y-intercept b
3. The equation of the line y = mx + b
4. The coordinates of the points where the line crosses the x-axis and the y-axis
5. The value of y when x = 5

In Python, use the fractions module from the standard library to calculate exactly, and show the formulas you used and the numbers from the execution result. If an answer is a fraction, give it in lowest terms.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula

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\(y = mx + b\)	y equals m x plus b	The slope-intercept form of a linear function: \(m\) is the slope and \(b\) is the y-intercept. This is the standard form in US schools. (Some countries write it \(y = ax + b\).)
\(m\)	m	The slope (rate of change): how much y increases each time x increases by 1. Nobody knows for sure why the letter m is used for slope.
\(b\)	b	The y-intercept: the value of y when x = 0, which is the height where the graph crosses the y-axis.
\(x_1,\ y_1\)	x sub 1, y sub 1	The coordinates of point 1. The small number at the lower right is called a subscript; it is a label for "which point" (it is not multiplication or an exponent).
\(\Delta\)	delta	The capital Greek letter delta, the Greek D, as in "difference". It stands for "change". \(\Delta x\) is the change in x and \(\Delta y\) is the change in y.
\(\left(-\dfrac{b}{m},\ 0\right)\)	negative b over m, zero	The point where the line crosses the x-axis. Its y-coordinate is 0, and its x-coordinate is \(-\dfrac{b}{m}\), the solution of the equation \(mx + b = 0\).
\((0,\ b)\)	zero, b	The point where the line crosses the y-axis. Its x-coordinate is 0, and its y-coordinate is the y-intercept \(b\) itself.

linear function	A function of the form \(y = mx + b\). Its graph is a straight line. The word "linear" tells you that x appears only to the first power. Taught in Grade 8.
function	A rule that gives back exactly one number for each number you put in. Think of it as a machine: put in \(x\) and out comes \(y\). For example, put 3 into the machine \(y = 2x + 1\) and 7 comes out.
slope	A number that tells "how much the line goes up or down for every 1 it goes across" (rise over run). A positive slope rises from left to right, a negative slope falls, and a slope of 0 gives a horizontal line.
rate of change	The change in y divided by the change in x, \(\dfrac{\Delta y}{\Delta x}\). For a linear function it is the same wherever you measure it, and it equals the slope \(m\).
y-intercept	The y-coordinate of the point where the graph crosses the y-axis (the value of y when x = 0). In the linear function \(y = mx + b\), it is \(b\). (The x-intercept is where the graph crosses the x-axis.)
direct variation	A relationship of the form \(y = kx\) (a proportional relationship). When x doubles or triples, y doubles or triples too. It is the special linear function whose y-intercept \(b\) is 0 (its line passes through the origin). Taught in Grade 7.
coordinates	A pair of numbers \((x,\ y)\) that gives the position of a point. The horizontal position is the x-coordinate and the vertical position is the y-coordinate.
coordinate plane	A plane made by crossing a horizontal number line (the x-axis) and a vertical number line (the y-axis) at a right angle. It is the grid you draw graphs on.
origin	The point \((0,\ 0)\) where the x-axis and the y-axis cross. It is written \(O\), from "origin".
crossing point	The point where two lines cross. On this page, you find the points where a line crosses the x-axis and the y-axis.
change in y	How much a value increased, found as "after − before" (the change in x is found the same way). If the value went down, the change is negative.
constant	A fixed number that does not change. In an equation such as "x = 2", the 2 is a constant, and the equation stands for the vertical line whose x-coordinate is always 2.
constant function	A function whose y-value is always the same, whatever x is. Its equation has the form \(y = b\), and its graph is a horizontal line parallel to the x-axis. It is \(y = mx + b\) with \(m = 0\); some textbooks count it as a linear function and some do not.

Linear Function Calculator (Find y = mx + b from Two Points or a Slope and a Point, Rate of Change and Intercepts)

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