Answer
$y - 2 = -\frac{1}{2}(x - 6)$
Work Step by Step
We are given the points $(6, 2)$ and $(2, 4)$.
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:
$m = \frac{4 - 2}{2 - 6}$
Subtract the numerator and denominator to simplify:
$m = \frac{2}{-4}$
Divide the numerator and denominator by their greatest common denominator, which is $2$:
$m = -\frac{1}{2}$
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:
$y - 2 = -\frac{1}{2}(x - 6)$
This equation is now in point-slope form.
