Find the x and y Intercepts y=(4x)/(x+5)

$y = \frac{4 x}{x + 5}$

Find the x-intercepts.

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

$0 = \frac{4 x}{x + 5}$

Solve the equation.

Set the numerator equal to zero.

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{4 (0)}{(0) + 5}$

Solve the equation.

Remove parentheses.

$y = \frac{4 (0)}{0 + 5}$

Remove parentheses.

$y = \frac{4 (0)}{(0) + 5}$

Simplify $\frac{4 (0)}{(0) + 5}$ .

Cancel the common factor of $0$ and $(0) + 5$ .

Factor $5$ out of $4 (0)$ .

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

Cancel the common factors.

Factor $5$ out of $0$ .

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

Factor $5$ out of $5$ .

$y = \frac{5 (4 \cdot (0))}{5 \cdot 0 + 5 \cdot 1}$

Factor $5$ out of $5 \cdot 0 + 5 \cdot 1$ .

$y = \frac{5 (4 \cdot (0))}{5 \cdot (0 + 1)}$

Cancel the common factor.

$y = \frac{5 (4 \cdot (0))}{5 \cdot (0 + 1)}$

Rewrite the expression.

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

Multiply $4$ by $0$ .

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

Simplify the expression.

Add $0$ and $1$ .

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

Divide $0$ by $1$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the x and y Intercepts y=(4x)/(x+5)

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