Question

Which of the equations below shows the relationship between d and p?

Answer 1

We are given a graph of a relationship between total price (p) and time (d)

Since the graph seems to be linear, the general form of such a graph is given by

`p=md+b_{}`

Where m is the slope and b is the y-intercept.

The y-intercept is the point where the line intersects the y-axis.

From the graph, we see that the line intersects the y-axis at 30

So, the y-intercept is 30

`b=30`

The slope of the line is given by

`m=\frac{\text{rise}}{\text{run}}`

The rise is the vertical distance between the two points on the line.

The run is the horizontal distance between the two points on the line.

As you can see, we selected two points on the graph. ( you may select any other)

The rise is 40 and the run is 2, so the slope is

`m=\frac{\text{rise}}{\text{run}}=(40)/(2)=20`

So, the slope of the line is 20

Therefore, the equation of the line becomes

`\begin{gathered} p=md+b_{} \\ p=20d+30 \end{gathered}`

Option D is the correct answer.