Algebra Examples

$\frac{3}{4} x - \frac{1}{5} y = \frac{- 1}{5}$

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 left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} - \frac{1}{5} y = \frac{- 1}{5}$

Step 2.1.1.2

Combine $y$ and $\frac{1}{5}$ .

$\frac{3 x}{4} - \frac{y}{5} = \frac{- 1}{5}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Move the negative in front of the fraction.

$\frac{3 x}{4} - \frac{y}{5} = - \frac{1}{5}$

Step 2.3

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$- \frac{y}{5} = - \frac{1}{5} - \frac{3 x}{4}$

Step 2.4

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{y}{5}) = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5

Simplify both sides of the equation.

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Step 2.5.1

Simplify the left side.

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Step 2.5.1.1

Simplify $- 5 (- \frac{y}{5})$ .

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Step 2.5.1.1.1

Cancel the common factor of $5$ .

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Step 2.5.1.1.1.1

Move the leading negative in $- \frac{y}{5}$ into the numerator.

$- 5 \frac{- y}{5} = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5.1.1.1.2

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- y}{5} = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5.1.1.1.3

Cancel the common factor.

$5 \cdot - 1 \frac{- y}{5} = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5.1.1.1.4

Rewrite the expression.

$- - y = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5.1.1.2

Multiply.

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Step 2.5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5.1.1.2.2

Multiply $y$ by $1$ .

$y = - 5 (- \frac{1}{5} - \frac{3 x}{4})$

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

Simplify $- 5 (- \frac{1}{5} - \frac{3 x}{4})$ .

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Step 2.5.2.1.1

Apply the distributive property.

$y = - 5 (- \frac{1}{5}) - 5 (- \frac{3 x}{4})$

Step 2.5.2.1.2

Cancel the common factor of $5$ .

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Step 2.5.2.1.2.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$y = - 5 (\frac{- 1}{5}) - 5 (- \frac{3 x}{4})$

Step 2.5.2.1.2.2

Factor $5$ out of $- 5$ .

$y = 5 (- 1) \frac{- 1}{5} - 5 (- \frac{3 x}{4})$

Step 2.5.2.1.2.3

Cancel the common factor.

$y = 5 \cdot - 1 \frac{- 1}{5} - 5 (- \frac{3 x}{4})$

Step 2.5.2.1.2.4

Rewrite the expression.

$y = - - 1 - 5 (- \frac{3 x}{4})$

Step 2.5.2.1.3

Multiply $- 1$ by $- 1$ .

$y = 1 - 5 (- \frac{3 x}{4})$

Step 2.5.2.1.4

Multiply $- 5 (- \frac{3 x}{4})$ .

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Step 2.5.2.1.4.1

Multiply $- 1$ by $- 5$ .

$y = 1 + 5 \frac{3 x}{4}$

Step 2.5.2.1.4.2

Combine $5$ and $\frac{3 x}{4}$ .

$y = 1 + \frac{5 (3 x)}{4}$

Step 2.5.2.1.4.3

Multiply $3$ by $5$ .

$y = 1 + \frac{15 x}{4}$

Step 2.6

Reorder $1$ and $\frac{15 x}{4}$ .

$y = \frac{15 x}{4} + 1$

Step 2.7

Reorder terms.

$y = \frac{15}{4} x + 1$