Susan R. answered • 12/07/20

Certified and Experienced High School Mathematics teacher with M.Ed

A scatter plot of data showing the percentage of total Internet users who visited an online store on a given day in December includes the points (2008, 2.0) and (2010, 4.5). Write the slope-intercept form of an equation for the line of fit.

Hi Abdul,

You can find the slope of any line if you have two points. Use the slope formula: difference of y values (subtract the y values) and divide by the difference in x-values (subtract the x values).

Since the x-values for your problems are years, we usually convert the year to a more normal value, like 0, 1, 2, 3, etc. To do this, pick any year to be "year zero". I would pick 2008 as "year zero". This would make 2008 into "year 0" and 2010 into "year 2". Your two points would turn into (0,2) and (2,4.5).

slope m is (4.5-2)/(2-0)=2.5/2=1.25.

slope-intercept equation y=mx+b

We now have the slope to substitute in: y=1.25x+b.

Since Year zero is 2008, (0,2) is a point on the line and 2 is your y-intercept.

So your final equation is y=1.25x+2 **where x stands for the number of years that have passed since 2008. **

You can check your answer by putting 2 in for x to see what happens two years after 2008. In other words, 2010. If your equation is correct, you should get the y-value of 4.5. This works. Check it out.

Note that you could have set ANY year as "year zero". But it's easier if you use the first given year because then you also get the y-intercept without any work :-). But most importantly, keep track of what year you are setting as your year zero!