Question

A scatter plot of data showing the percentage of fatal internet users who visit a video sharing site on a given day in December includes the points ( 2010, 17.0) and ( 2008, 0.3) . Write the slope intercept form of an equation for the line of fit containing those points.

Answer 1

Given the points

`\begin{gathered} (x_1,y_1)=(2010,17) \\ \text{and} \\ (x_2,y_2)=(2008,0.3) \end{gathered}`

we will find the slope m and the y-intercept b.

The slope m is given as

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{that is,} \\ m=(0.3-17)/(2008-2010) \end{gathered}`

which gives

`\begin{gathered} m=(-16.7)/(-2) \\ m=8.35 \end{gathered}`

Then, the line equation in slope-intercept form is

`y=8.35x+b`

In order to find the y-intercept b, we can substitute one of the given point, for instance, by replacing point (2010,17) in the last result, we have

`17=8.35(2010)+b`

which gives

`\begin{gathered} 17=16783.5+b \\ \text{then} \\ b=17-16783.5 \\ b=-16766.5 \end{gathered}`

Then, the answer is

`y=8.35x-16766.5`