Find the x and y Intercepts r(x)=(2x+8)/(-8x+4)

$r (x) = \frac{2 x + 8}{- 8 x + 4}$

Find the x-intercepts.

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

$0 = \frac{2 x + 8}{- 8 x + 4}$

Solve the equation.

Set the numerator equal to zero.

$2 x + 8 = 0$

Solve the equation for $x$ .

Subtract $8$ from both sides of the equation.

$2 x = - 8$

Divide each term in $2 x = - 8$ by $2$ and simplify.

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x = - 4$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{2 (0) + 8}{- 8 \cdot 0 + 4}$

Solve the equation.

Remove parentheses.

$y = \frac{2 (0) + 8}{- 8 \cdot 0 + 4}$

Simplify $\frac{2 (0) + 8}{- 8 \cdot 0 + 4}$ .

Cancel the common factor of $2 (0) + 8$ and $- 8 \cdot 0 + 4$ .

Reorder terms.

$y = \frac{2 (0) + 8}{4 - 8 \cdot 0}$

Factor $4$ out of $2 (0)$ .

$y = \frac{4 (2 \cdot (0)) + 8}{4 - 8 \cdot 0}$

Factor $4$ out of $8$ .

$y = \frac{4 (2 \cdot (0)) + 4 \cdot 2}{4 - 8 \cdot 0}$

Factor $4$ out of $4 (2 \cdot (0)) + 4 (2)$ .

$y = \frac{4 (2 \cdot (0) + 2)}{4 - 8 \cdot 0}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = \frac{4 (2 \cdot (0) + 2)}{4 (1) - 8 \cdot 0}$

Factor $4$ out of $- 8 \cdot 0$ .

$y = \frac{4 (2 \cdot (0) + 2)}{4 (1) + 4 (- 2 \cdot 0)}$

Factor $4$ out of $4 (1) + 4 (- 2 \cdot 0)$ .

$y = \frac{4 (2 \cdot (0) + 2)}{4 (1 - 2 \cdot 0)}$

Cancel the common factor.

$y = \frac{4 (2 \cdot (0) + 2)}{4 (1 - 2 \cdot 0)}$

Rewrite the expression.

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

Simplify the numerator.

Multiply $2$ by $0$ .

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

Add $0$ and $2$ .

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

Simplify the denominator.

Multiply $- 2$ by $0$ .

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

Add $1$ and $0$ .

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

Divide $2$ by $1$ .

$y = 2$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the x and y Intercepts r(x)=(2x+8)/(-8x+4)

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