If the data point is at (3,10.5) and the prediction equation is y=-6.1x+12.5, what is the residual for this data point ?

We can extract the points (3, 21) and (6, 12) from the graph.

First we are going to find the slope of the line passing through those points. To do it, we are using the slope formula:

where

is the slope of the line

are the coordinates of the first point

are the coordinates of the second point

Our first point is (3, 21) and our second point is (6, 12), so let's replace the values

Now, to find the equation of the line in point, slope, we are using the point-slope formula:

where

is the slope of the line

are the coordinates of the first point.

Since we have the slope, let's replace the values:

Next, to find the equation in slope-intercept form, we just need to solve our point-slope equation for :

Answer

Equation of the line in point-slope form:

Equation of the line in slope-intercept form:

The time that initially took Scoot  to deliver his packages is the time it took him to deliver the packages in his first day of work. In the hist day of word, zero days has passed since he begin working, so .

It initially took Scoot 30 minutes to deliver his packages.

Now, since the slope of our line is negative 3, Scott's delivery time decreases 3 minutes per day.

Answer

It initially took Scoot 30 minutes to deliver his packages.

Scott's delivery time decreases 3 minutes per day.