Definition: Slope-intercept form is the equation y = mx + b of a line, where m is the slope and b is the y-intercept.
What is it?
It is a way to write a line so that both key features show. In y = mx + b, m tells the steepness and b tells where the line starts on the y-axis.
How do you read it?
In y = -3x + 7, the slope is -3 and the y-intercept is 7. Start at (0, 7), then go down 3 and right 1, repeatedly.
How do you write one?
Given slope 5/2 and passing through (0, -4), write y = (5/2)x – 4. Given two points, (1, 3) and (4, 12): slope = 9/3 = 3, then 3 = 3(1) + b gives b = 0, so y = 3x.
How do you convert to it?
Solve for y. From 6x + 2y = 10, subtract 6x: 2y = -6x + 10. Divide by 2: y = -3x + 5.
Why is it useful?
You can graph quickly and compare lines. Parallel lines share the same m.
What is a common mistake?
Dividing only one term when solving for y. In 2y = -6x + 10, you must divide both terms by 2.
Where to learn it
- Solving Multi-Step Linear Equations – lesson
- Modeling Real Situations With Linear Functions – lesson