Algebra Examples

$\frac{x - 4}{- 4 x - 16}$

Step 1

Write $\frac{x - 4}{- 4 x - 16}$ as an equation.

$y = \frac{x - 4}{- 4 x - 16}$

Step 2

Find the x-intercepts.

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Step 2.1

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

$0 = \frac{x - 4}{- 4 x - 16}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$x - 4 = 0$

Step 2.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.3

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = \frac{(0) - 4}{- 4 \cdot 0 - 16}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{0 - 4}{- 4 \cdot 0 - 16}$

Step 3.2.2

Remove parentheses.

$y = \frac{(0) - 4}{- 4 \cdot 0 - 16}$

Step 3.2.3

Simplify $\frac{(0) - 4}{- 4 \cdot 0 - 16}$ .

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Step 3.2.3.1

Reduce the expression by cancelling the common factors.

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Step 3.2.3.1.1

Cancel the common factor of $(0) - 4$ and $- 4 \cdot 0 - 16$ .

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Step 3.2.3.1.1.1

Factor $4$ out of $0$ .

$y = \frac{4 (0) - 4}{- 4 \cdot 0 - 16}$

Step 3.2.3.1.1.2

Factor $4$ out of $- 4$ .

$y = \frac{4 \cdot 0 + 4 \cdot - 1}{- 4 \cdot 0 - 16}$

Step 3.2.3.1.1.3

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

$y = \frac{4 \cdot (0 - 1)}{- 4 \cdot 0 - 16}$

Step 3.2.3.1.1.4

Cancel the common factors.

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Step 3.2.3.1.1.4.1

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

$y = \frac{4 \cdot (0 - 1)}{4 (- 0) - 16}$

Step 3.2.3.1.1.4.2

Factor $4$ out of $- 16$ .

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

Step 3.2.3.1.1.4.3

Factor $4$ out of $4 (- 0) + 4 (- 4)$ .

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

Step 3.2.3.1.1.4.4

Cancel the common factor.

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

Step 3.2.3.1.1.4.5

Rewrite the expression.

$y = \frac{0 - 1}{- 0 - 4}$

Step 3.2.3.1.2

Subtract $1$ from $0$ .

$y = \frac{- 1}{- 0 - 4}$

Step 3.2.3.2

Simplify the denominator.

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Step 3.2.3.2.1

Multiply $- 1$ by $0$ .

$y = \frac{- 1}{0 - 4}$

Step 3.2.3.2.2

Subtract $4$ from $0$ .

$y = \frac{- 1}{- 4}$

Step 3.2.3.3

Dividing two negative values results in a positive value.

$y = \frac{1}{4}$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{4})$

Step 4

List the intersections.

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

y-intercept(s): $(0, \frac{1}{4})$

Step 5