Find the x and y Intercepts r(x)=(2x+6)/(-6x+3)

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

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$2 x + 6 = 0$

Solve the equation for $x$ .

Subtract $6$ from both sides of the equation.

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

Cancel the common factor of $2 (0) + 6$ and $- 6 \cdot 0 + 3$ .

Factor $3$ out of $2 (0)$ .

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

Factor $3$ out of $6$ .

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

Factor $3$ out of $3 (2 \cdot (0)) + 3 (2)$ .

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

Cancel the common factors.

Factor $3$ out of $- 6 \cdot 0$ .

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

Factor $3$ out of $3$ .

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

Factor $3$ out of $3 (- 2 \cdot 0) + 3 (1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Multiply $2$ by $0$ .

$y = \frac{0 + 2}{- 2 \cdot 0 + 1}$

Add $0$ and $2$ .

$y = \frac{2}{- 2 \cdot 0 + 1}$

Simplify the denominator.

Multiply $- 2$ by $0$ .

$y = \frac{2}{0 + 1}$

Add $0$ and $1$ .

$y = \frac{2}{1}$

Divide $2$ by $1$ .

$y = 2$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(- 3, 0)$

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

Find the x and y Intercepts r(x)=(2x+6)/(-6x+3)

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