Algebra Examples

$\frac{15 - x}{x - 10}$

Step 1

Write $\frac{15 - x}{x - 10}$ as an equation.

$y = \frac{15 - x}{x - 10}$

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 $x$ .

$0 = \frac{15 - x}{x - 10}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$15 - x = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Subtract $15$ from both sides of the equation.

$- x = - 15$

Step 2.2.2.2

Divide each term in $- x = - 15$ by $- 1$ and simplify.

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Step 2.2.2.2.1

Divide each term in $- x = - 15$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 15}{- 1}$

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 15}{- 1}$

Step 2.2.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 15}{- 1}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $- 15$ by $- 1$ .

$x = 15$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(15, 0)$

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 $y$ .

$y = \frac{15 - (0)}{(0) - 10}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{15 - (0)}{0 - 10}$

Step 3.2.2

Remove parentheses.

$y = \frac{15 - (0)}{(0) - 10}$

Step 3.2.3

Simplify $\frac{15 - (0)}{(0) - 10}$ .

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Step 3.2.3.1

Cancel the common factor of $15 - (0)$ and $(0) - 10$ .

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Step 3.2.3.1.1

Rewrite $15$ as $- 1 (- 15)$ .

$y = \frac{- 1 (- 15) - (0)}{(0) - 10}$

Step 3.2.3.1.2

Factor $- 1$ out of $- 1 (- 15) - (0)$ .

$y = \frac{- 1 (- 15 + 0)}{(0) - 10}$

Step 3.2.3.1.3

Factor $5$ out of $- 1 (- 15 + 0)$ .

$y = \frac{5 (- 1 (- 3 + 0))}{0 - 10}$

Step 3.2.3.1.4

Cancel the common factors.

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Step 3.2.3.1.4.1

Factor $5$ out of $0$ .

$y = \frac{5 (- 1 (- 3 + 0))}{5 (0) - 10}$

Step 3.2.3.1.4.2

Factor $5$ out of $- 10$ .

$y = \frac{5 (- 1 (- 3 + 0))}{5 \cdot 0 + 5 \cdot - 2}$

Step 3.2.3.1.4.3

Factor $5$ out of $5 \cdot 0 + 5 \cdot - 2$ .

$y = \frac{5 (- 1 (- 3 + 0))}{5 \cdot (0 - 2)}$

Step 3.2.3.1.4.4

Cancel the common factor.

$y = \frac{5 (- 1 (- 3 + 0))}{5 \cdot (0 - 2)}$

Step 3.2.3.1.4.5

Rewrite the expression.

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

Step 3.2.3.2

Simplify the expression.

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Step 3.2.3.2.1

Add $- 3$ and $0$ .

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

Step 3.2.3.2.2

Subtract $2$ from $0$ .

$y = \frac{- 1 \cdot - 3}{- 2}$

Step 3.2.3.2.3

Multiply $- 1$ by $- 3$ .

$y = \frac{3}{- 2}$

Step 3.2.3.2.4

Move the negative in front of the fraction.

$y = - \frac{3}{2}$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{2})$

Step 4

List the intersections.

x-intercept(s): $(15, 0)$

y-intercept(s): $(0, - \frac{3}{2})$

Step 5