Answer
0 = $\frac{-1}{3}$x - $\frac{1}{5}$y + 1
Work Step by Step
The intercept form of an equation is:
$\frac{x}{a}$ + $\frac{y}{b}$ = 1 where a is (a,0), the x-intercept, and b is (0,b), the y-intercept.
In this problem the x-intercept is (3,0), so a = 3
In this problem the y-intercept is (0, 5), so b = 5
Using the equation above for the intercept form, we have:
$\frac{x}{3}$ + $\frac{y}{5}$ = 1
We want to manipulate the equation to be in the general form which is:
0 = ax + by + c
Note: a, b, and c are constants.
First, we want to get the left hand side to be 0. We can do this by subtracting $\frac{x}{3}$ from each side, and subtracting $\frac{y}{5}$ from each side.
$\frac{x}{3}$ + $\frac{y}{5}$ - $\frac{x}{3}$ - $\frac{y}{5}$ = 1 - $\frac{x}{3}$ - $\frac{y}{5}$
This gets:
0 = 1 - $\frac{x}{3}$ - $\frac{y}{5}$
We can rearrange the variables to get the general form:
0 = $\frac{-1}{3}$x - $\frac{1}{5}$y + 1
