Find the x and y Intercepts -2(x-3y)=12

$- 2 (x - 3 y) = 12$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$- 2 (x - 3 \cdot 0) = 12$

Solve the equation.

Simplify.

Multiply $- 3$ by $0$ .

$- 2 (x + 0) = 12$

Add $x$ and $0$ .

$- 2 x = 12$

Divide each term in $- 2 x = 12$ by $- 2$ and simplify.

Divide each term in $- 2 x = 12$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Divide $x$ by $1$ .

$x = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x = - 6$

x-intercept(s) in point form.

x-intercept(s): $(- 6, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$- 2 ((0) - 3 y) = 12$

Solve the equation.

Simplify.

Subtract $3 y$ from $0$ .

$- 2 (- 3 y) = 12$

Multiply $- 3$ by $- 2$ .

$6 y = 12$

Divide each term in $6 y = 12$ by $- 2$ and simplify.

Divide each term in $6 y = 12$ by $- 2$ .

$\frac{6 y}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $6$ and $- 2$ .

Factor $2$ out of $6 y$ .

$\frac{2 (3 y)}{- 2} = \frac{12}{- 2}$

Move the negative one from the denominator of $\frac{3 y}{- 1}$ .

$- 1 \cdot (3 y) = \frac{12}{- 2}$

Simplify the expression.

Rewrite $- 1 \cdot (3 y)$ as $- (3 y)$ .

$- (3 y) = \frac{12}{- 2}$

Multiply $3$ by $- 1$ .

$- 3 y = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$- 3 y = - 6$

Divide each term in $- 3 y = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

x-intercept(s): $(- 6, 0)$

y-intercept(s): $(0, 2)$

Step 4

Find the x and y Intercepts -2(x-3y)=12

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