Samir created a scatter plot and drew a line of best fit, as shown.

What is the equation of the line of best fit that Samir drew?

Work Shown:

We will only focus on the two points that are on the regression line.

Those two points are (3,10) and (12,4)

Let (x1,y1) = (3,10) and (x2,y2) = (12,4)

Find the slope of the line through (x1,y1) = (3,10) and (x2,y2) = (12,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 10)/(12 - 3)

m = -6/9

m = -2/3

Plug m = -2/3 and (x1,y1) = (3,10) into the point slope formula

Solve for y.

y - y1 = m(x - x1)

y - 10 = (-2/3)(x - 3)

y - 10 = (-2/3)x + (-2/3)(-3) ... distribute

y - 10 = (-2/3)x + 2

y - 10 + 10 = (-2/3)x + 2 + 10 add 10 to both sides

y = (-2/3)x + 12

This matches up with what the graph shows because the regression line intersects 12 on the y axis, so the y intercept is 12.

y = (-2/3)x + 12 is in the form y = mx+b with m = -2/3 as the slope and b = 12 as the y intercept.

true? is that what you're asking or do you mean something else?