Slope-Intercept Form (y = mx + b)
Slope-intercept form is the most useful way to write a linear equation. The equation y = mx + b immediately tells you two things: the slope (how steep the line is) and where it crosses the y-axis. Most graphing and analysis starts here.
m is the slope (rise over run) and b is the y-intercept (where the line crosses the y-axis). In y = 2x + 3: the line rises 2 units for every 1 unit right, and crosses the y-axis at (0, 3).
In this lesson
1 What m and b Mean
In y = mx + b, every part has a specific geometric meaning that makes the equation immediately readable.
y = 3x − 4: slope is 3 (rises 3 units per unit right), y-intercept is −4 (crosses y-axis at (0,−4)). y = −x + 7: slope is −1 (falls 1 unit per unit right), y-intercept is 7. You can graph either line immediately from this information.
2 How to Graph from Slope-Intercept Form
Graphing y = mx + b takes two steps: plot the y-intercept, then use the slope to find a second point.
m = 3 means go up 3 for every 1 right , not right 3 for every 1 up. If m = 3/4, you go up 3 and right 4. Getting this backwards gives you a completely different line.
Try the Slope Calculator
Find the slope and equation of any line from two points.
3 Writing the Equation from Two Points
Given two points, you can find the slope-intercept equation in two steps: calculate the slope, then find b.
4 Converting from Standard Form
Standard form (Ax + By = C) can be converted to slope-intercept form by solving for y.
5 Real-World Applications
Any situation where something changes at a constant rate can be modeled with slope-intercept form. A plumber who charges $50 per hour plus a $75 call-out fee: total cost y = 50x + 75, where x is hours. The slope (50) is the hourly rate, the y-intercept (75) is the fixed fee.
Cell phone data: if you start with 10GB and use 0.5GB per day, remaining data y = −0.5x + 10. The negative slope shows depletion, the y-intercept is the starting amount, and you can immediately solve for when you run out (y = 0 → x = 20 days).
Practice Problems
Sources & Further Reading
The explanations on this page draw on the following established sources. We link to primary and secondary sources so you can verify claims and go deeper on any topic.