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

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

Find the x-intercepts.

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

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

Solve the equation.

Rewrite the equation as $\frac{2}{3} x - 6 = 0$ .

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

Combine $\frac{2}{3}$ and $x$ .

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

Add $6$ to both sides of the equation.

$\frac{2 x}{3} = 6$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 6$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 6$

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{3}{2} \cdot 6$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x = \frac{3}{2} \cdot (2 (3))$

Cancel the common factor.

$x = \frac{3}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$x = 3 \cdot 3$

Multiply $3$ by $3$ .

$x = 9$

x-intercept(s) in point form.

x-intercept(s): $(9, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Multiply $\frac{2}{3}$ by $0$ .

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

Remove parentheses.

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

Simplify $\frac{2}{3} \cdot (0) - 6$ .

Multiply $\frac{2}{3}$ by $0$ .

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(9, 0)$

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

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

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