Answer
0 = $\frac{-3}{2}$x + $\frac{1}{2}$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 ($\frac{2}{3}$,0), so a = $\frac{2}{3}$
In this problem the y-intercept is (0, -2), so b = -2
Using the equation above for the intercept form, we have:
$\frac{x}{\frac{2}{3}}$ + $\frac{y}{-2}$ = 1
Which can be rewritten as:
$\frac{3x}{2}$ + $\frac{y}{-2}$ = 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 $\frac{3x}{2}$ from each side, and subtracting $\frac{y}{-2}$ from each side.
$\frac{3x}{2}$ + $\frac{y}{-2}$ - $\frac{3x}{2}$ - $\frac{y}{-2}$ = 1 - $\frac{3x}{2}$ - $\frac{y}{-2}$
This gets:
0 = 1 - $\frac{3x}{2}$ - $\frac{y}{-2}$
We can rearrange the variables to get the general form:
0 = $\frac{-3}{2}$x + $\frac{1}{2}$y + 1
