Hi there!
[tex]\large\boxed{2, -9}[/tex]
We can create an equation for the line PR using the given coordinates. Use the following formula for the slope:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the coordinates for P and R:
[tex]m = \frac{-5-(-1)}{-1-(-4)} = -\frac{4}{3}[/tex]
Find the equation by using point-slope form:
y - y1 = m(x - x1)
Plug in a coordinate and the slope:
y - (-5) = -4/3(x - ( - 1))
Simplify:
y + 5 = -4/3(x + 1)
To find the y-coordinate if x = 2, plug in the x value:
y + 5 = -4/3(2 + 1)
y + 5 = -4/3(3)
y + 5 = -4
y = -9
Thus, the coordinate is (2, -9)
