Question

find the value of x so (x,-3) is collinear to (6,7) and (-2,-5). Show all work.

Answer 1

You want (x,-3) to be on the same straight line as the other two points.

Figure out the equation for that straight line. The slope is [7 - (-5)/[6 - (-2)] = 3/2

The line equation is y = (3/2)x + b
The value of b is given by
7 = (3/2)6 + b = 9 + b
Therefore b = -2 and the line equation is

y = (3/2)x - 2

Now if the point (x,-3) is going to be on that line, we must have

-3 = (3/2)x -2
3/2 x = -1
x = -2/3

Answer 2

OR

their slopes have to be equal

(-3-7)/(x-6) = (-5-7)/(-2-6)
-10/(x-6) = -12/-8
-12x + 72 = 80
-12x = 8
x = -8/12 = -2/3