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

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{that is,} \\ m=\frac{0.3-17}{2008-2010} \end{gathered}$

which gives

$\begin{gathered} m=\frac{-16.7}{-2} \\ m=8.35 \end{gathered}$

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

$y=8.35x-16766.5$