Slope-intercept form is y = mx + b. The number m is the slope, and b is the y-intercept, the height where the line crosses the y-axis. Once an equation is in this form, you can graph it at a glance.
Try it with your own problem ↓
The steps
- To read a line: m (the number in front of x) is the slope, and b (the number added at the end) is where it crosses the y-axis.
- To convert another form, get y alone: move the x term to the other side by adding or subtracting.
- Divide every term by the number in front of y.
- To graph: plot (0, b), then use the slope as rise over run to find more points.
- To write an equation from the slope m and a point, put them in y = mx + b and solve for b.
A worked example
Write 2x + 3y = 6 in slope-intercept form.
- Subtract 2x from both sides: 3y = −2x + 6.
- Divide every term by 3: y = (−2/3)x + 2.
- Read it: slope m = −2/3 and y-intercept b = 2.
- To graph: plot (0, 2), then go down 2 and right 3 to reach (3, 0). Check: 2(3) + 3(0) = 6. ✓
y = −(2/3)x + 2.
Common mistakes
- Dividing only one term by 3. Divide every term on the right side.
- Mixing up m and b. m multiplies x. b is the term with no x.
- Losing the minus sign. Subtracting 2x gives −2x, so the slope is negative.
- Plotting the intercept on the x-axis. b is where the line crosses the y-axis, at (0, b).
Questions people ask
What is the y-intercept?
The point where the line crosses the y-axis, where x = 0. In y = mx + b it is (0, b).
How do I find the equation from two points?
Find the slope from the two points, then use one point to solve for b in y = mx + b.
What are the other forms of a line?
Standard form (Ax + By = C) and point-slope form (y − y₁ = m(x − x₁)).
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