Question

This scatter plot shows the relationship between the number of oil changes a car has per year and the average engine repair costs in a year for a sample population The y-intercept of the estimated line of the best fit is at (0,b).Enter the approximate value of b in the first response box Enter the approximate slope of the estimated line that best fits in the second response box

Answer 1

We have a scatter plot and a line of best fit to the points of the scatter plot.

To solve the first part we need to find the value of b.

Step 1. The y-intercept (0,b) is the point where the line crosses the y-axis, shown as a red point in the following image:

First, lets complete the values of the y-axis to see which point is the red point (the y-intercept):

Each step of the grid represents 40, so we complete the values by adding 40 to the previous value on the grid.

As we can see the y-intercept is at:

`(0,360)`

Comparing with (0,b) the value of b is 360:

`b=360`

Step 2. Now we have to find the approximate slope of the line.

To find the slope we take two points where the line crosses by the corners of the grid:

We take the two green points and label them as follows:

`\begin{gathered} x_1=0 \\ y_1=360 \\ x_2=4 \\ y_2=240 \end{gathered}`

Now we use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where m is the slope.

Substituting the known values:

`m=(240-360)/(4-0)=(-120)/(4)=-30`

The slope is -30.

Answer:

b=360 and slope=-30