Find the x and y Intercepts 1/3x-1/6y=-2/3

$\frac{1}{3} x - \frac{1}{6} y = - \frac{2}{3}$

Step 1

Find the x-intercepts.

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

$\frac{1}{3} x - \frac{1}{6} \cdot 0 = - \frac{2}{3}$

Solve the equation.

Simplify $\frac{1}{3} x - \frac{1}{6} \cdot 0$ .

Simplify each term.

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} - \frac{1}{6} \cdot 0 = - \frac{2}{3}$

Multiply $- \frac{1}{6} \cdot 0$ .

Multiply $0$ by $- 1$ .

$\frac{x}{3} + 0 (\frac{1}{6}) = - \frac{2}{3}$

Multiply $0$ by $\frac{1}{6}$ .

$\frac{x}{3} + 0 = - \frac{2}{3}$

Add $\frac{x}{3}$ and $0$ .

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 2$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$\frac{1}{3} \cdot (0) - \frac{1}{6} y = - \frac{2}{3}$

Solve the equation.

Simplify $\frac{1}{3} \cdot (0) - \frac{1}{6} y$ .

Simplify each term.

Multiply $\frac{1}{3}$ by $0$ .

$0 - \frac{1}{6} y = - \frac{2}{3}$

Combine $y$ and $\frac{1}{6}$ .

$0 - \frac{y}{6} = - \frac{2}{3}$

Subtract $\frac{y}{6}$ from $0$ .

$- \frac{y}{6} = - \frac{2}{3}$

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{y}{6}) = - 6 (- \frac{2}{3})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 6 (- \frac{y}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{y}{6}$ into the numerator.

$- 6 \frac{- y}{6} = - 6 (- \frac{2}{3})$

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- y}{6} = - 6 (- \frac{2}{3})$

Cancel the common factor.

$6 \cdot - 1 \frac{- y}{6} = - 6 (- \frac{2}{3})$

Rewrite the expression.

$- - y = - 6 (- \frac{2}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 6 (- \frac{2}{3})$

Multiply $y$ by $1$ .

$y = - 6 (- \frac{2}{3})$

Simplify the right side.

Simplify $- 6 (- \frac{2}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$y = - 6 (\frac{- 2}{3})$

Factor $3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$y = 4$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts 1/3x-1/6y=-2/3

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