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

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

Step 1

Write $\frac{6 x - 6}{x + 2}$ as an equation.

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$6 x - 6 = 0$

Solve the equation for $x$ .

Add $6$ to both sides of the equation.

$6 x = 6$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $6$ .

$x = 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

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

Factor $2$ out of $6 (0)$ .

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

Factor $2$ out of $- 6$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $0$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 \cdot 0 + 2 \cdot 1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Multiply $3$ by $0$ .

$y = \frac{0 - 3}{0 + 1}$

Subtract $3$ from $0$ .

$y = \frac{- 3}{0 + 1}$

Simplify the expression.

Add $0$ and $1$ .

$y = \frac{- 3}{1}$

Divide $- 3$ by $1$ .

$y = - 3$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(1, 0)$

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

Step 5

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

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