What is slope-intercept form?

Slope-intercept form is 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). It is the most common way to write linear equations because you can read the slope and intercept directly.

How do you find the x-intercept from y = mx + b?

Set y = 0 and solve for x: 0 = mx + b, so x = -b/m. The x-intercept is the point (-b/m, 0). If m = 0 (horizontal line), there is no x-intercept unless b = 0.

What makes two lines perpendicular?

Two lines are perpendicular if their slopes multiply to -1, meaning m1 × m2 = -1, or equivalently m2 = -1/m1. For example, lines with slopes 2 and -1/2 are perpendicular and meet at a 90° angle.

Linear Equation Explorer

Drag the slope and intercept sliders. See the slope triangle, intercepts, and equation update in real time.

y = mx + b

Presets

Slope m = 1.0

1.0

y-intercept b = 0.0

0.0

Show

Parallel line Perpendicular line

Properties

Equation	--
Slope	--
y-intercept	--
x-intercept	--
Direction	--

The Math Behind It

Slope-Intercept Form

Standard form: y = mx + b
m = slope = rise / run
b = y-intercept (where line crosses y-axis)
x-intercept: set y=0, solve x = -b/m

Slope

Positive slope: line rises left to right
Negative slope: line falls left to right
Zero slope: horizontal line
Undefined slope: vertical line (not a function)

Parallel & Perpendicular

Parallel lines have equal slopes: m₁ = m₂
Perpendicular lines: m₁ × m₂ = -1
Perpendicular slope = -1/m

Try This

Set m=0 — horizontal line at y=b
Set b=0 — line passes through origin
Toggle perpendicular — see the 90° angle
Click Animate — watch the slope rotate

Linear Equation Explorer

y = mx + b

Properties

The Math Behind It

Slope-Intercept Form

Slope

Parallel & Perpendicular

Try This

Related Visualizations

Systems of Equations

Quadratic Explorer

All Visualizations

You're crushing it!