4.4 Understand Slope of a Line

Before you get started, take this readiness quiz.

Simplify: $\frac{1 – 4}{8 - 2}$.
If you missed this problem, review the reference.

Divide: $\frac{0}{4} , \frac{4}{0}$.
If you missed this problem, review the reference.

Simplify: $\frac{15}{−3} , \frac{−15}{3} , \frac{−15}{−3}$.
If you missed this problem, review the reference.

Find the slope of each line:

ⓐ $x = 8$ ⓑ $y = −5$.

Find the slope of the line: $x = −4 .$

Find the slope of the line: $y = 7 .$

Use the slope formula to find the slope of the line through the points: $\left(8 , 5\right)$ and $\left(6 , 3\right)$.

Use the slope formula to find the slope of the line through the points: $\left(1 , 5\right)$ and $\left(5 , 9\right)$.

Use the slope formula to find the slope of the line through the points: $\left(−3 , 4\right)$ and $\left(2 , −1\right) .$

Use the slope formula to find the slope of the line through the pair of points: $\left(−2 , 6\right)$ and $\left(−3 , −4\right)$.

Use the example, substituting the rise = 14 and run = 24.

Use the example, substituting rise = 15 and run = 36.

Find the slope of a pipe that slopes down $\frac{1}{3}$ inch per foot.

Find the slope of a pipe that slopes down $\frac{3}{4}$ inch per yard.

Find the slope of each line.

$y = 3$

Find the slope of each line.

$x = 4$

Find the slope of each line.

$y = −2$

Find the slope of each line.

$x = −5$

Use the slope formula to find the slope of the line between each pair of points.

$\left(1 , 4\right) , \left(3 , 9\right)$

Use the slope formula to find the slope of the line between each pair of points.

$\left(0 , 3\right) , \left(4 , 6\right)$

Use the slope formula to find the slope of the line between each pair of points.

$\left(2 , 5\right) , \left(4 , 0\right)$

Use the slope formula to find the slope of the line between each pair of points.

$\left(−3 , 3\right) , \left(4 , −5\right)$

Use the slope formula to find the slope of the line between each pair of points.

$\left(−1 , −2\right) , \left(2 , 5\right)$

Use the slope formula to find the slope of the line between each pair of points.

$\left(4 , −5\right) , \left(1 , −2\right)$

Road grade. A local road has a grade of 6%. The grade of a road is its slope expressed as a percent. Find the slope of the road as a fraction and then simplify. What rise and run would reflect this slope or grade?

Wheelchair ramp. The rules for wheelchair ramps require a maximum 1-inch rise for a 12-inch run.

1. ⓐ How long must the ramp be to accommodate a 24-inch rise to the door?
2. ⓑ Create a model of this ramp.

What does the sign of the slope tell you about a line?

Why is the slope of a vertical line “undefined”?