Mathematics
Slope-Intercept Form
Slope-intercept form is y = mx + b — where m is the slope (rise over run) and b is the y-intercept (where the line crosses the y-axis). It's the most useful linear form for graphing.
How to Approach Slope-Intercept Form
Find the slope (m)
Pick two points (x₁, y₁) and (x₂, y₂). Slope m = (y₂ - y₁) / (x₂ - x₁). Equivalent to 'rise over run' — vertical change divided by horizontal change.
Find the y-intercept (b)
Plug a known point and m into y = mx + b and solve for b. Or look at the graph — b is the y-coordinate where the line crosses the y-axis.
Write y = mx + b
Substitute m and b. To graph: start at (0, b), then move up m and right 1 to plot the next point.
Frequently Asked Questions
What if the slope is undefined?+
Vertical lines have undefined slope (you'd divide by zero). They can't be written as y = mx + b — they're written as x = c instead.
How do I convert from standard form?+
Standard form is Ax + By = C. Solve for y: y = (-A/B)x + C/B. The slope is -A/B and the y-intercept is C/B.
What does negative slope mean?+
The line falls from left to right. As x increases, y decreases. The steepness depends on the absolute value of m.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
Stuck on a Slope-Intercept Form problem?
Snap a photo or type the question. ScanSolve walks you through every step — same as the worked examples above. 5 free solves per day, no card required.