<h3>Answer: Choice D</h3><h3>y = (-1/5)x + 7</h3>
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Work Shown:
We will only focus on the two points that are on the regression line.
Those two points are (10,5) and (15,4)
Let (x1,y1) = (10,5) and (x2,y2) = (15,4)
Find the slope of the line through (x1,y1) = (10,5) and (x2,y2) = (15,4)
m = (y2 - y1)/(x2 - x1)
m = (4 - 5)/(15 - 10)
m = -1/5
m = -0.2
Plug m = -0.2, and (x1,y1) = (10,5) into the point slope formula. Solve for y
y - y1 = m(x - x1)
y - 5 = -0.2(x - 10)
y - 5 = -0.2*x - 0.2*(-10) ... distribute
y - 5 = -0.2*x + 2
y - 5+5 = -0.2*x + 2 + 5 ... add 5 to both sides
y = -0.2*x + 7
y = (-1/5)*x + 7 .... convert -0.2 to -1/5
The equation y = (-1/5)x + 7 is in the form y = mx+b with m = -1/5 = -0.2 as the slope and b = 7 as the y intercept. The y intercept is where the graph crosses the vertical y axis. More specifically, the location of the y intercept in this case is at the point (0,7).
