Answer
$y - 5 = \frac{1}{4}(x - 3)$
Work Step by Step
We are given the points $(-5, 3)$ and $(3, 5)$.
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 the values into this formula:
$m = \frac{5 - 3}{3 - (-5)}$
Subtract the numerator and denominator to simplify:
$m = \frac{2}{8}$
Divide the numerator and denominator by their greatest common denominator, which is $2$:
$m = \frac{1}{4}$
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:
$y - 5 = \frac{1}{4}(x - 3)$
This equation is now in point-slope form.
