Answer: Slope = -2/3
===================================================
Explanation:
Let's compute the slope of the line through the two original points
m = (y2-y1)/(x2-x1)
m = (4-10)/(7-(-2))
m = (4-10)/(7+2)
m = -6/9
m = (-2*3)/(3*3)
m = -2/3
The slope is -2/3
-------------
Now apply the scale factor.
We'll multiply each coordinate of each point by 2
(-2,10) becomes (-4,20) after multiplying each coordinate by 2
(7,4) becomes (14,8) after multiplying each coordinate by 2
Let's find the slope of the line through (-4,20) and (14,8)
m = (y2-y1)/(x2-x1)
m = (8-20)/(14-(-4))
m = (8-20)/(14+4)
m = -12/18
m = (-2*6)/(3*6)
m = -2/3
We get the same slope. This isn't a coincidence. Dilating a set of points will preserve the slope of the line through those points.
If A and B are the two original points, and A' and B' are the dilated counterparts, then the slope of line AB is the same as the slope of line A'B'.
The scale factor doesn't affect the answer.
