Answer
0 = 6x + $\frac{3}{2}$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 ($\frac{-1}{6}$,0), so a = $\frac{-1}{6}$
In this problem the y-intercept is (0, $\frac{-2}{3}$), so b = $\frac{-2}{3}$
Using the equation above for the intercept form, we have:
$\frac{x}{\frac{-1}{6}}$ + $\frac{y}{\frac{-2}{3}}$ = 1
Which can be rewritten as:
$\frac{6x}{-1}$ + $\frac{3y}{-2}$ = 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 $\frac{6x}{-1}$ from each side, and subtracting $\frac{3y}{-2}$ from each side.
$\frac{6x}{-1}$ + $\frac{3y}{-2}$ - $\frac{6x}{-1}$ - $\frac{3y}{-2}$ = 1 - $\frac{6x}{-1}$ - $\frac{3y}{-2}$
This gets:
0 = 1 - $\frac{6x}{-1}$ - $\frac{3y}{-2}$
We can rearrange the variables to get the general form:
0 = 6x + $\frac{3}{2}$y + 1
