Answer
$y - 2 = \frac{4}{3}(x - 3)$
$y = \frac{4}{3}x - 2$
Work Step by Step
We are given the two points $(0, -2)$ and $(3, 2)$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let's plug in the values into this formula:
$m = \frac{2 - (-2)}{3 - 0}$
Subtract the numerator and denominator to simplify:
$m = \frac{4}{3}$
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:
$y - y_1 = m(x - x_1)$
Let's plug in the points and slope into the formula:
$y - 2 = \frac{4}{3}(x - 3)$
To change this equation into slope-intercept form, we need to isolate $y$.
First, use distribution to simplify:
$y - 2 = \frac{4}{3}x - \frac{4}{3}(3)$
Multiply to simplify:
$y - 2 = \frac{4}{3}x - \frac{12}{3}$
Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is $3$:
$y - 2 = \frac{4}{3}x - 4$
To isolate $y$, we add $2$ to each side of the equation:
$y = \frac{4}{3}x - 4 + 2$
Add the constants to simplify:
$y = \frac{4}{3}x - 2$
Now, we have the equation of the line in slope-intercept form.
