Find the x and y Intercepts (5x)/(-2x-4)

$\frac{5 x}{- 2 x - 4}$

Step 1

Write $\frac{5 x}{- 2 x - 4}$ as an equation.

$y = \frac{5 x}{- 2 x - 4}$

Step 2

Find the x-intercepts.

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

$0 = \frac{5 x}{- 2 x - 4}$

Solve the equation.

Set the numerator equal to zero.

$5 x = 0$

Divide each term in $5 x = 0$ by $5$ and simplify.

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Divide $x$ by $1$ .

$x = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x = 0$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = \frac{5 (0)}{- 2 \cdot 0 - 4}$

Solve the equation.

Remove parentheses.

$y = \frac{5 (0)}{- 2 \cdot 0 - 4}$

Simplify $\frac{5 (0)}{- 2 \cdot 0 - 4}$ .

Reduce the expression by cancelling the common factors.

Cancel the common factor of $0$ and $- 2 \cdot 0 - 4$ .

Reorder terms.

$y = \frac{5 (0)}{- 4 - 2 \cdot 0}$

Factor $2$ out of $5 (0)$ .

$y = \frac{2 (5 \cdot (0))}{- 4 - 2 \cdot 0}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 (5 \cdot (0))}{2 (- 2) - 2 \cdot 0}$

Factor $2$ out of $- 2 \cdot 0$ .

$y = \frac{2 (5 \cdot (0))}{2 (- 2) + 2 (- 0)}$

Factor $2$ out of $2 (- 2) + 2 (- 0)$ .

$y = \frac{2 (5 \cdot (0))}{2 (- 2 - 0)}$

Cancel the common factor.

$y = \frac{2 (5 \cdot (0))}{2 (- 2 - 0)}$

Rewrite the expression.

$y = \frac{5 \cdot (0)}{- 2 - 0}$

Cancel the common factor of $0$ and $- 2 - 0$ .

Rewrite $- 2$ as $- 1 (2)$ .

$y = \frac{5 \cdot (0)}{- 1 (2) - 0}$

Factor $- 1$ out of $- 0$ .

$y = \frac{5 \cdot (0)}{- 1 (2) - (0)}$

Factor $- 1$ out of $- 1 (2) - (0)$ .

$y = \frac{5 \cdot (0)}{- 1 (2 + 0)}$

Factor $2$ out of $5 \cdot (0)$ .

$y = \frac{2 (5 \cdot (0))}{- 1 (2 + 0)}$

Cancel the common factors.

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

$y = \frac{2 (5 \cdot (0))}{2 (- 1 (1 + 0))}$

Cancel the common factor.

$y = \frac{2 (5 \cdot (0))}{2 (- 1 (1 + 0))}$

Rewrite the expression.

$y = \frac{5 \cdot (0)}{- 1 (1 + 0)}$

Multiply $5$ by $0$ .

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

Simplify the expression.

Add $1$ and $0$ .

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

Multiply $- 1$ by $1$ .

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

Divide $0$ by $- 1$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5

Find the x and y Intercepts (5x)/(-2x-4)

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