11.4 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:

1. ⓐ $x = 8$
2. ⓑ $y = −5$

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

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

Find the slope of the line through the given points: $\left(8 , 5\right)$ and $\left(6 , 3\right) .$

Find the slope of the line through the given points: $\left(1 , 5\right)$ and $\left(5 , 9\right) .$

Find the slope of the line through the pair of points: $\left(−3 , 4\right)$ and $\left(2 , −1\right) .$

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

Find the slope given rise and run: A roof with a rise $= 14$ and run $= 24 .$

Find the slope given rise and run: A roof with a rise $= 15$ and run $= 36 .$

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

Find the slope of the pipe: The pipe 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.

$\left(−3 , 3\right) , \left(2 , −5\right)$

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.

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

Solve these slope applications.

Road grade A local road has a grade of $\text{6}\% .$ The grade of a road is its slope expressed as a percent.

1. ⓐ Find the slope of the road as a fraction and then simplify the fraction.
2. ⓑ 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. ⓐ What run must the ramp have to accommodate a $\text{24}-\text{inch}$ rise to the door?
2. ⓑ Draw 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?

Find the ordered pairs that are solutions to the given equation.

$5 x + y = 10$

1. ⓐ $\left(5 , 1\right)$
2. ⓑ $\left(2 , 0\right)$
3. ⓒ $\left(4 , −10\right)$

Complete the table to find solutions to each linear equation.

$y = 4 x - 1$

Complete the table to find solutions to each linear equation.

$x + 2 y = 5$

Find three solutions to each linear equation.

$x + y = 3$

Find three solutions to each linear equation.

$y = 3 x + 1$

Find the intercepts.

$x - y = −1$

Find the intercepts.

$y = 3 x$

Identify the most convenient method to graph each line.

$y = −3$

Identify the most convenient method to graph each line.

$x - y = 2$

Identify the most convenient method to graph each line.

$y = \frac{3}{4} x - 1$

Find the slope of each line.

$x = 5$

Find the slope of each line.

$y = −1$

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

$\left(−1 , −1\right) , \left(0 , −5\right)$

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

$\left(−5 , −2\right) , \left(3 , 2\right)$

Is $\left(1 , 3\right)$ a solution to the equation $x + 4 y = 12 ?$ How do you know?

Complete the table to find three solutions to the equation $4 x + y = 8$

Find the slope of each line.

Find the slope of the line $y = 2 .$

Find the slope of each line.

A bicycle route climbs $20$ feet for $1,000$ feet of horizontal distance. What is the slope of the route?