Precalculus Examples

$y - \frac{3}{4} = - 2 (x + \frac{1}{3})$

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

Simplify the right side.

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Step 2.1.1

Simplify $- 2 (x + \frac{1}{3})$ .

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Step 2.1.1.1

Apply the distributive property.

$y - \frac{3}{4} = - 2 x - 2 (\frac{1}{3})$

Step 2.1.1.2

Combine $- 2$ and $\frac{1}{3}$ .

$y - \frac{3}{4} = - 2 x + \frac{- 2}{3}$

Step 2.1.1.3

Move the negative in front of the fraction.

$y - \frac{3}{4} = - 2 x - \frac{2}{3}$

Step 2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.1

Add $\frac{3}{4}$ to both sides of the equation.

$y = - 2 x - \frac{2}{3} + \frac{3}{4}$

Step 2.2.2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - 2 x - \frac{2}{3} \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.2.3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - 2 x - \frac{2}{3} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{3}{3}$

Step 2.2.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.4.1

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$y = - 2 x - \frac{2 \cdot 4}{3 \cdot 4} + \frac{3}{4} \cdot \frac{3}{3}$

Step 2.2.4.2

Multiply $3$ by $4$ .

$y = - 2 x - \frac{2 \cdot 4}{12} + \frac{3}{4} \cdot \frac{3}{3}$

Step 2.2.4.3

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$y = - 2 x - \frac{2 \cdot 4}{12} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 2.2.4.4

Multiply $4$ by $3$ .

$y = - 2 x - \frac{2 \cdot 4}{12} + \frac{3 \cdot 3}{12}$

Step 2.2.5

Combine the numerators over the common denominator.

$y = - 2 x + \frac{- 2 \cdot 4 + 3 \cdot 3}{12}$

Step 2.2.6

Simplify the numerator.

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Step 2.2.6.1

Multiply $- 2$ by $4$ .

$y = - 2 x + \frac{- 8 + 3 \cdot 3}{12}$

Step 2.2.6.2

Multiply $3$ by $3$ .

$y = - 2 x + \frac{- 8 + 9}{12}$

Step 2.2.6.3

Add $- 8$ and $9$ .

$y = - 2 x + \frac{1}{12}$