Algebra Examples

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

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 $- 2 (x - \frac{1}{4})$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

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

Step 2.1.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.1.2.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 2.1.1.1.2.2

Factor $2$ out of $- 2$ .

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

Step 2.1.1.1.2.3

Factor $2$ out of $4$ .

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

Step 2.1.1.1.2.4

Cancel the common factor.

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

Step 2.1.1.1.2.5

Rewrite the expression.

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

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Move the negative in front of the fraction.

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

Step 2.1.1.2.2

Multiply $- 1 (- \frac{1}{2})$ .

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Step 2.1.1.2.2.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.2.2.2

Multiply $\frac{1}{2}$ by $1$ .

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

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 $\frac{2}{3}$ to both sides of the equation.

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

Step 2.2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.2.3

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

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

Step 2.2.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.4.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 2.2.4.2

Multiply $2$ by $3$ .

$y = - 2 x + \frac{3}{6} + \frac{2}{3} \cdot \frac{2}{2}$

Step 2.2.4.3

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

$y = - 2 x + \frac{3}{6} + \frac{2 \cdot 2}{3 \cdot 2}$

Step 2.2.4.4

Multiply $3$ by $2$ .

$y = - 2 x + \frac{3}{6} + \frac{2 \cdot 2}{6}$

Step 2.2.5

Combine the numerators over the common denominator.

$y = - 2 x + \frac{3 + 2 \cdot 2}{6}$

Step 2.2.6

Simplify the numerator.

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Step 2.2.6.1

Multiply $2$ by $2$ .

$y = - 2 x + \frac{3 + 4}{6}$

Step 2.2.6.2

Add $3$ and $4$ .

$y = - 2 x + \frac{7}{6}$