Find the x and y Intercepts 6x+3y=-8

$6 x + 3 y = - 8$

Step 1

Find the x-intercepts.

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

$6 x + 3 (0) = - 8$

Solve the equation.

Simplify $6 x + 3 (0)$ .

Multiply $3$ by $0$ .

$6 x + 0 = - 8$

Add $6 x$ and $0$ .

$6 x = - 8$

Divide each term in $6 x = - 8$ by $6$ and simplify.

Divide each term in $6 x = - 8$ by $6$ .

$\frac{6 x}{6} = \frac{- 8}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 8}{6}$

Divide $x$ by $1$ .

$x = \frac{- 8}{6}$

Simplify the right side.

Cancel the common factor of $- 8$ and $6$ .

Factor $2$ out of $- 8$ .

$x = \frac{2 (- 4)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 4}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot - 4}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{- 4}{3}$

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{4}{3}, 0)$

Step 2

Find the y-intercepts.

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

$6 (0) + 3 y = - 8$

Solve the equation.

Simplify $6 (0) + 3 y$ .

Multiply $6$ by $0$ .

$0 + 3 y = - 8$

Add $0$ and $3 y$ .

$3 y = - 8$

Divide each term in $3 y = - 8$ by $3$ and simplify.

Divide each term in $3 y = - 8$ by $3$ .

$\frac{3 y}{3} = \frac{- 8}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 8}{3}$

Divide $y$ by $1$ .

$y = \frac{- 8}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{8}{3})$

Step 3

List the intersections.

x-intercept(s): $(- \frac{4}{3}, 0)$

y-intercept(s): $(0, - \frac{8}{3})$

Step 4

Find the x and y Intercepts 6x+3y=-8

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