Question

chase earns $10 per hour as a waiter. his earnings are modeled using a straight - line on a coordinate plane.
points a, b, and c form △abc. use the triangle to complete each statement.
the length of $overline{bc}$ is 40. the length of $overline{ac}$ is 4.
the slope of $overline{ab}$ is the height - to - width ratio of △abc.
enter the slope of $overline{ab}$:
points b, d, and e form △bde. use the triangle to complete each statement.
enter the length of $overline{de}$:
enter the length of $overline{be}$:
the slope of $overline{bd}$ is the height - to - width ratio of △bde.
enter the slope of $overline{bd}$:
the slope of a straight line is the same between any two points on the line. so, the slope of the line that shows chases earnings is

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{\text{rise}}{\text{run}}=\frac{y_2 - y_1}{x_2 - x_1}$. For $\triangle ABC$, if the height (rise) of $\overline{BC}$ is 40 and the width (run) of $\overline{AC}$ is 4, then the slope of $\overline{AB}$ is $\frac{40}{4}$.

Step2: Calculate slope of $\overline{AB}$

$\frac{40}{4}=10$.

For $\triangle BDE$:

Step3: Determine length of $\overline{DE}$

From the graph, if we assume the vertical - distance between $D$ and $E$ is 60 (by looking at the y - values on the graph). So the length of $\overline{DE}$ is 60.

Step4: Determine length of $\overline{BE}$

The horizontal distance between $B$ and $E$ is 6 (by looking at the x - values on the graph). So the length of $\overline{BE}$ is 6.

Step5: Calculate slope of $\overline{BD}$

Using the slope formula $m=\frac{\text{rise}}{\text{run}}$, with rise = 60 and run = 6, we get $\frac{60}{6}=10$.

Since the slope of a straight - line is the same between any two points on the line, the slope of the line that shows Chase's earnings is also 10.

Answer:

Slope of $\overline{AB}$: 10
Length of $\overline{DE}$: 60
Length of $\overline{BE}$: 6
Slope of $\overline{BD}$: 10
Slope of the line for Chase's earnings: 10