Answer
$y = -\frac{1}{2}x + 3$
Work Step by Step
We are given the points $A(0, 3)$ and $B(6, 0)$.
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:
$m = \frac{0 - 3}{6 - 0}$
Subtract the numerator and denominator to simplify:
$m = \frac{-3}{6}$
Divide the numerator and denominator by their greatest common denominator, which is $3$:
$m = -\frac{1}{2}$
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:
$y - 0 = -\frac{1}{2}(x - 6)$
Let's use the distributive property:
$y = -\frac{1}{2}x - (\frac{1}{2})(-6)$
Multiply to simplify:
$y = -\frac{1}{2}x + \frac{6}{2}$
Divide both the numerator and denominator of $\frac{6}{2}$ by their greatest common factor, $2$:
$y = -\frac{1}{2}x + 3$
