Find the x and y Intercepts -3x+2y=12

$- 3 x + 2 y = 12$

Step 1

Find the x-intercepts.

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

$- 3 x + 2 (0) = 12$

Solve the equation.

Simplify $- 3 x + 2 (0)$ .

Multiply $2$ by $0$ .

$- 3 x + 0 = 12$

Add $- 3 x$ and $0$ .

$- 3 x = 12$

Divide each term in $- 3 x = 12$ by $- 3$ and simplify.

Divide each term in $- 3 x = 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{12}{- 3}$

Divide $x$ by $1$ .

$x = \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$x = - 4$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0)$

Step 2

Find the y-intercepts.

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

$- 3 \cdot 0 + 2 y = 12$

Solve the equation.

Simplify $- 3 \cdot 0 + 2 y$ .

Multiply $- 3$ by $0$ .

$0 + 2 y = 12$

Add $0$ and $2 y$ .

$2 y = 12$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $12$ by $2$ .

$y = 6$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 4, 0)$

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

Step 4

Find the x and y Intercepts -3x+2y=12

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