Question

(4,6) (10,15) (-2, ??)
collinear
PLEASE SHOW ALL WORK

Answer 1

slope of line joining first 2 points=9/6=3/2
slope of line joining last 2 points=15-y/12
as both are equal
we get y=-3

Answer 2

Equate the two slopes using the first and second point coordinates\[\frac{y-6}{x-4}=\frac{y-15}{x-10}\]and solve for y. The resulting expression is the line equation passing through the first two points.\[y=\frac{3 x}{2} \]Replace x with -2 above to obtain the third points y coordinate.\[y=\frac{3 x}{2} \to y=\frac{3(-2)}{2}\to y=-3 \]