Math 1 · Unit 3 · Lesson 2 · part 2 of 8
Two numbers, two jobs
Every straight line can be written in one form:
Two numbers, two jobs
Every straight line can be written in one form:
Two numbers, two jobs. b is the y-intercept: where the line crosses the y-axis, the value of y when x is 0. m is the slope from Lesson 1: the rate of change, rise over run, how much y goes up or down for each step x takes to the right. The form is called slope-intercept form because it shows both numbers right in the equation.
Why b is where it crosses the y-axis
The y-axis is the line where x = 0. Put x = 0 into y = mx + b: the mx part becomes m × 0 = 0, so y = 0 + b = b. Whatever m is, the line passes through (0, b). That is why b is both the y-intercept and the starting value of the line.
Why m is the slope
Step x from 0 to 1: y goes from b to m + b. It changed by m. Step again: y changes by m again. Every step of 1 to the right changes y by exactly m. That is rise over run with a run of 1: the slope.