Question

The graph shows the distance a car traveled, y, in x hours:

A coordinate plane graph is shown. The x-axis is labeled time in hours ,and the y-axis is labeled distance in miles. The line passes through the points 2 comma 60, and 4 comma 120.

What is the rise-over-run value for the relationship represented in the graph?

20
30
1 over 20
1 over 30

Answer 1

Answer:

The correct answer is 30

Step-by-step explanation:

Given: The x-axis represents the time in hours and the y-axis represents the distance in miles.

The line passes through the points $(2,60)$ and $(4,120)$

To find: The rise-over-run value for the relationship in the graph.

$\begin{aligned}m &=\frac{R i s e}{R u n} \\&=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&=\frac{120-60}{4-2} \\&=\frac{60}{2} \\&=30\end{aligned}$

Thus, the rise-over-run value for the relationship represented in the graph is 30.

Answer 2

You can use the fact that the rise over run is calculated based on difference in y values over difference in corresponding x values

The rise-over-run value for the relationship represented in the graph is given by

Option

What is rise-over-run relationship and why is it needed?

Firstly there are graphs of functions. We usually take x axis horizontal and y axis vertical to that horizontal axis.

When seeing the graph, it feels like the horizontal axis (x - axis) is ground and the y axis is the height.

When we plot a graph, we see how many points were increased on x axis for which how many points were increased in y axis. It is needed for many cases to get to know the rate at which the y values are increasing compared to x values.

This is taken by:

$Slope = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{rise}{run}$

where slope is representing rate and $(x_1,y_1),$ is initial data point and $(x_2,y_2)$ is next data point. We see how much y increased(height increased or say rise of the y value) for how much increment in x axis (or say run over the horizontal ground of x axis).

Using that above method to obtain the rise-over-run relationship for the given graph

$(x_1, y_1) = (2,60)\\(x_2, y_2) = (4, 120)$

$Slope = \dfrac{120 - 60}{4-2} = \dfrac{60}{2} = 30$

This shows that as we run 1 unit on x axis forward(forward direction is right to the graph or up to the graph with respect to the origin of the graph, and it is taken positive), the point y will rise 30 units on y axis.

The plot is given below.

Learn more about rise over run relationship here:

https://brainly.com/question/2832483