Lesson 8 of 1524
Slope, intercept, and graphs
A straight line is y = mx + b. m is the slope. b is the y-intercept.
Practice this chapterThe slope is rise over run: how much y changes when x increases by 1. A slope of 2 means y goes up 2 for each step to the right.
The y-intercept is the value of y when x is 0. In y = mx + b, that value is b.
From two points, subtract the y-values and divide by the difference of the x-values, in the same order.
Slope from two points
m = (y₂ − y₁) / (x₂ − x₁)
Change in y, divided by change in x.
Worked example
For y = 2x + 1, find y when x = 3, and name the slope.
- 1Substitute 3 for x: y = 2(3) + 1.
- 2Multiply before you add: 2 × 3 = 6, then 6 + 1 = 7. So the point is (3, 7).
- 3In y = mx + b, the number multiplied by x is the slope, and the added number is the y-intercept.
- 4Here m = 2 and b = 1. When x increases by 1, y increases by 2. When x is 0, y is 1.
Result: y = 7, and the slope is 2
Why. The 2 in front of x is the slope, the rate of change. The value 7 is the height of the line at x = 3. It is not the slope, and the +1 is the height where the line crosses the y-axis.
The intercept is not the slope. In y = −x + 4 the slope is −1 and the intercept is 4.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.