Question

A scatter plot contains the points (2, 8) and (19, 59). Write an equation in slope-intercept form for the best-fit line of the scatter plot.

Answer 1

This isn't hard at all. First, since we have two points and we're finding the best fit line for a scatterplot, then we are using the equation y=mx+b. Knowing this, we must find what our slope is. In order to find the slope, we use the slope intercept formula, which is \[\frac{ f(b) - f(a) }{ b - a }\]
Our formula would look like\[\frac{ 59-8 }{ 19-2 }\]
Which is equivalent to 3. Therefore, we currently have y=3x+b.
To find our b value, we simply need to find the y-intercept. Since we know that this is a linear function, we can simply start from (2,8) and work our way back to 0. Because we know the y coordinate at 2 and we know that the slope is 3, we can simply do 8-2(3), where the 2 is the scalar factor used to get the x value to 0. Therefore, we find that our b=2. So our equation is y=3x+2.