Math Problem Solution

To solve this problem, we first need to find the slope between point A and point B. The formula for the slope between two points (x₁, y₁) and (x₂, y₂) is:

slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of points A and B:

• Point A is (-7, 2)
• Point B is (8, -14)

The differences in the coordinates are:

• y₂ - y₁ = -14 - 2 = -16
• x₂ - x₁ = 8 - (-7) = 8 + 7 = 15

So, the slope is:

slope = -16 / 15

Next, we find how much the x-coordinate increases from point B to point C. The increase in x is 2, so the change in y is:

change in y = 2 * (-16 / 15) = -32 / 15

Converting -32/15 to a mixed number:

-32/15 = -2 2/15

Thus, the y-coordinate increases by -2 2/15.

Finally, we add this change to the y-coordinate of point B to find the y-coordinate of point C:

yₓ = -14 + (-2 2/15) = -16 2/15

Converting this to an improper fraction:

yₓ = -11 13/15

Therefore, the y-coordinate of point C is -11 13/15.