Question

slope and rate of change student handout
the side - view of two ramps at a local skate park are shown.
a. what measurement do the ramps have in common?
b. what measurement is different between the ramps?
c. which ramp appears steeper? justify your answer using a and b.
slope

• when a linear relationship is graphed, the slope is a value used to describe the

______ of the line.

• slope is the ratio of the ____ change compared to the __ change, or \\(\frac{rise}{run}\\). slope is equal to the __ of ____ of the graph and the linear relationship.

types of slope
a ____ slope increases from left to right. a __ slope decreases from left to right. a __ slope is a horizontal line. an ____ slope is a vertical line.
finding slope from a graph

• choose two ______ on the graphed line.
• draw a right triangle to count the ____ and the ____ between the points.
• set up a ______ of \\(\frac{rise}{run}\\) and simplify.
• double check if the graph is ______ or

Explanation:

Step1: Analyze common measurement

For two ramps with height 8 ft each, the common measurement is the vertical - height.
The vertical height of both ramps is 8 ft.

Step2: Analyze different measurement

The horizontal lengths are different. Ramp A has a horizontal length of 12 ft and ramp B has a horizontal length of 8 ft.

Step3: Determine steeper ramp

The slope of a ramp is calculated as $\text{slope}=\frac{\text{rise}}{\text{run}}$. For ramp A, slope $m_A=\frac{8}{12}=\frac{2}{3}$. For ramp B, slope $m_B = \frac{8}{8}=1$. Since $1>\frac{2}{3}$, ramp B is steeper.

Answer:

a. The vertical height (8 ft) is the common measurement.
b. The horizontal length is different (12 ft for ramp A and 8 ft for ramp B).
c. Ramp B appears steeper. Justification: The slope of ramp A is $\frac{2}{3}$ and the slope of ramp B is 1, and $1>\frac{2}{3}$.