Answer
$y + 2 = \frac{3}{4}(x - 3)$
Work Step by Step
We are given the points $E(3, -2)$ and $F(-5, -8)$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$,
where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
Let's plug in these values into this formula:
$m = \frac{-8 - (-2)}{-5 - 3}$
Subtract the numerator and denominator to simplify:
$m = \frac{-6}{-8}$
Let's divide the numerator and denominator by their greatest common factor, $-2$:
$m = \frac{3}{4}$
Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$,
where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
Let's plug in the points and slope into the formula:
$y - (-2) = \frac{3}{4}(x - 3)$
Simplify the signs:
$y + 2 = \frac{3}{4}(x - 3)$
