Slope-Intercept Form (y = mx + b): How to Find and Use It
Quick answer: Slope-intercept form is y = mx + b. The number m is the slope, which tells you how steep the line is. The number b is the y-intercept, where the line crosses the y-axis. To write the equation, find m with (y₂ − y₁) ÷ (x₂ − x₁), substitute one point to find b, then write y = mx + b.
What m and b mean
In y = 3x − 2, the slope is 3, so y goes up 3 for every 1 step right. The y-intercept is −2, so the line crosses the y-axis at (0, −2).
A positive slope rises left to right. A negative slope falls. A slope of 0 gives a flat line, y = b.
Finding the slope from two points
Slope = (y₂ − y₁) ÷ (x₂ − x₁), or "rise over run".
Find the slope through (1, 3) and (4, 9).
m = (9 − 3) ÷ (4 − 1) = 6 ÷ 3 = 2.
Writing the equation from two points
Carry on with the same points. Put m = 2 and (1, 3) into y = mx + b:
3 = 2(1) + b, so b = 1.
The equation is y = 2x + 1. Check with the other point: 2(4) + 1 = 9. It works.
Converting from standard form
Write 3x + 2y = 8 in slope-intercept form.
Get y on its own. Subtract 3x: 2y = −3x + 8. Divide by 2: y = −1.5x + 4.
So the slope is −1.5 and the line crosses the y-axis at 4.
Parallel and perpendicular lines
Parallel lines have the same slope. A line parallel to y = 2x + 1 through (0, −5) is y = 2x − 5.
Perpendicular lines have slopes that multiply to −1. A line perpendicular to y = 2x + 1 has slope −½.
A word problem
A phone plan costs a $20 activation fee plus $15 a month. Write an equation for the total cost, and find the cost after 6 months.
The monthly charge is the slope and the fee is the intercept: y = 15x + 20.
After 6 months: 15(6) + 20 = $110.
Linear models like this one turn up often on the SAT and PSAT math sections. See our digital SAT math guide.
Common mistakes
Swapping the order in the slope formula. Keep y₂ and x₂ from the same point.
Forgetting the sign when converting. Moving 3x across makes it −3x.
Mixing up b and the x-intercept. b is where the line meets the y-axis.
Dividing only one term. When you divide 2y = −3x + 8 by 2, divide both terms.
When extra support might help
Support is worth considering when graphs and equations don't connect yet, or when algebra slips are costing points on tests.
A tutor can't guarantee a score, but can build the habit of checking each step. Math Make Smart offers SAT preparation and PSAT preparation, and you can book a free trial lesson.
Frequently asked questions
What is slope-intercept form?
y = mx + b, where m is the slope and b is the y-intercept.
How do you find b?
Substitute the slope and one point into y = mx + b and solve for b.
What is the slope of a horizontal line?
0. Its equation is y = b.
Do parallel lines have the same slope?
Yes.