Find the x and y Intercepts -x+3y=6

$- x + 3 y = 6$

Step 1

Find the x-intercepts.

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

$- x + 3 (0) = 6$

Solve the equation.

Simplify $- x + 3 (0)$ .

Multiply $3$ by $0$ .

$- x + 0 = 6$

Add $- x$ and $0$ .

$- x = 6$

Divide each term in $- x = 6$ by $- 1$ and simplify.

Divide each term in $- x = 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{6}{- 1}$

Divide $x$ by $1$ .

$x = \frac{6}{- 1}$

Simplify the right side.

Divide $6$ by $- 1$ .

$x = - 6$

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 $y$ .

$- (0) + 3 y = 6$

Solve the equation.

Simplify $- (0) + 3 y$ .

Multiply $- 1$ by $0$ .

$0 + 3 y = 6$

Add $0$ and $3 y$ .

$3 y = 6$

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 -x+3y=6

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