Slope-intercept form calculator

Get y = mx + b from two points, a point and a slope, or standard form, with exact fractions and the line drawn for you.

x₁ y₁ x₂ y₂

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - (3)}{4 - (1)} = 2$

$3 = 2(1) + b$

$b = 3 - (2) = 1$

Equation

y = 2x + 1

Slope $2$ , y-intercept $(0, 1)$ , x-intercept (-0.5, 0).

Slope is rise over run

Point A

x-2

y-1

Point B

$m = \frac{\text{rise}}{\text{run}} = \frac{4 - (-1)}{3 - (-2)} = 1$

$y = 1x + 1$

Positive slope: the line rises left to right. Moving 1 step right changes y by 1.

the line
run = 5

How to graph a linear equation from y = mx + b

Plot the y-intercept $(0, b)$ .
From there, use the slope as rise over run. For $m = \tfrac{2}{3}$ , go up 2 and right 3 and plot a second point.
Draw a straight line through the two points and extend it both ways.

The three common forms of a line all describe the same thing: slope-intercept $y = mx + b$ , point-slope $y - y_1 = m(x - x_1)$ , and standard $Ax + By = C$ . Two lines together make a system of equations.

Frequently asked questions

What is slope-intercept form?

y = mx + b, where m is the slope (rise over run) and b is the y-intercept, the y-value where the line crosses the y-axis.

How do I find the equation of a line through two points?

Find the slope m = (y₂ − y₁)/(x₂ − x₁). Then substitute one point into y = mx + b and solve for b.

How do I convert Ax + By = C to slope-intercept form?

Solve for y: subtract Ax from both sides (By = −Ax + C), then divide by B, giving y = (−A/B)x + C/B.

What about vertical lines?

A vertical line like x = 3 has an undefined slope and can’t be written as y = mx + b. Horizontal lines have slope 0: y = b.