8th Grade Math - Graph Proportional Relationships, Interpreting the Unit Rate as the Slope: CCSS.Math.Content.8.EE.B.5

What is the slope of the line that passes through the points and ?

Explanation

The slope of a line is sometimes referred to as "rise over run." This is because the formula for slope is the change in y-value (rise) divided by the change in x-value (run). Therefore, if you are given two points, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , the slope of their line can be found using the following formula: $slope=(y_{1}-y_{2})/(x_{1}-x_{2})$

This gives us .

A line crosses the x-axis at and the y-axis at . What is the slope of this line?

$m=\frac{1}{3}$

$m=-\frac{1}{3}$

None of these.

Explanation

Given the points,

$\(x_1,y_1)=(0,6) \(x_2,y_2)=(6,8)$ .

We compute slope (m) as follows:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{6-0}=\mathbf{\frac{1}{3}}$

What is the slope of a line with an -intercept is and another -intercept of ?

$\infty$

Explanation

The -intercept is the value when .

Therefore, since the two -intercepts are and , the points are and .

Write the slope formula, plug in the values, and solve.

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{0-0}{6-4}= \frac{0}{2} =0$

The slope is zero.

Find the slope of the line that passes through the points:

and

$-\frac{1}{2}$

$\frac{7}{8}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{-20-4}{-10-2}$

Simplify.

$\text{Slope}=\frac{-24}{-12}$

Solve.

$\text{Slope}=2$

Find the slope of the line that passes through the points:

and

$\frac{4}{7}$

$\frac{3}{7}$

$-\frac{2}{7}$

$\frac{5}{7}$

Explanation

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{1-5}{-3-4}$

Simplify.

$\text{Slope}=\frac{-4}{-7}$

Solve.

$\text{Slope}=\frac{4}{7}$

Select the equation that shows the lowest unit rate.

Explanation

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

is always the slope, and is the -intercept.

We are looking for the equation with the lowest unit rate, or slope. Based on our options is the lowest value of ; thus our correct answer is

Select the equation that shows the lowest unit rate.

Explanation

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

is always the slope, and is the -intercept.

We are looking for the equation with the lowest unit rate, or slope. Based on our options is the lowest value of ; thus our correct answer is

Select the equation that shows the greatest unit rate.

Explanation

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

is always the slope, and is the -intercept.

We are looking for the equation with the greatest unit rate, or slope. Based on our options, is the greatest value of ; thus, our correct answer is

Select the equation that shows the lowest unit rate.

$y=\frac{1}{2}x+4$

$y=\frac{1}{3}x+5$

$y=\frac{1}{4}x+6$

$y=\frac{1}{5}x+7$

Explanation

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

is always the slope, and is the -intercept.

We are looking for the equation with the lowest unit rate, or slope. Based on our options $\frac{1}{5}$ is the lowest value of ; thus our correct answer is $y=\frac{1}{5}x+7$