The point-slope equation is [tex] (y - y_1) = m(x - x_1) [/tex], where [tex] m [/tex] is the slope of the line and [tex] (x_1, y_1) [/tex] is a point on the line.
First, we will need to find the slope, which has an equation of [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]. Substituting our points in, we find the slope of the line to be:
[tex] m = \dfrac{-61 - 27}{-8 - 3} = \dfrac{-88}{-11} = 8 [/tex]
Now, we can substitute all the values we know into the point-slope equation to find our result:
[tex] (y - 27) = 8(x - 3) = [y + (-27)] = 8[x + (-3)] [/tex]
The answers to the blanks (from left to right) are: -27, 8, -3
