Math 1 · Unit 3 · Lesson 2 · part 3 of 8
Read m and b off an equation
Reading m and b is mostly matching, with a few careful cases.
Read m and b off an equation
Reading m and b is mostly matching, with a few careful cases. m is the number multiplied on x. b is the number added (or subtracted) on its own.
| Equation | m (slope) | b (y-intercept) | Careful because |
|---|---|---|---|
| y = 2x + 3 | 2 | 3 | the plain case |
| y = x + 3 | 1 | 3 | a lonely x is 1x (the invisible 1 from Unit 1) |
| y = −2x | −2 | 0 | nothing added means b = 0: the line goes through the origin |
| y = 5 | 0 | 5 | no x term means m = 0: a flat line at height 5 |
| y = 4x − 7 | 4 | −7 | subtracting 7 is adding −7, so b is negative |
| y = −x + 2 | −1 | 2 | −x is (−1)x |
| y = 12x − 1 | 12 | −1 | a fraction slope: up 1 for every 2 right |
| y = 3 + 2x | 2 | 3 | the terms traded places (commutative property, Unit 1); m is still the number on x |
The two questionsWhich number is on the x? That is m. Which number stands alone? That is b. If there is no number on x, m is 1 (or −1 for −x). If nothing stands alone, b is 0. If there is no x at all, m is 0.