Algebra Examples

$- \frac{1}{5} x - 3 y = \frac{39}{5}$

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

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

$- \frac{x}{5} - 3 y = \frac{39}{5}$

Step 2.2

Add $\frac{x}{5}$ to both sides of the equation.

$- 3 y = \frac{39}{5} + \frac{x}{5}$

Step 2.3

Divide each term in $- 3 y = \frac{39}{5} + \frac{x}{5}$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 y = \frac{39}{5} + \frac{x}{5}$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{\frac{39}{5}}{- 3} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{\frac{39}{5}}{- 3} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{39}{5}}{- 3} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{39}{5} \cdot \frac{1}{- 3} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.2

Cancel the common factor of $3$ .

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Step 2.3.3.1.2.1

Factor $3$ out of $39$ .

$y = \frac{3 (13)}{5} \cdot \frac{1}{- 3} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.2.2

Factor $3$ out of $- 3$ .

$y = \frac{3 \cdot 13}{5} \cdot \frac{1}{3 \cdot - 1} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.2.3

Cancel the common factor.

$y = \frac{3 \cdot 13}{5} \cdot \frac{1}{3 \cdot - 1} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.2.4

Rewrite the expression.

$y = \frac{13}{5} \cdot \frac{1}{- 1} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.3

Multiply $\frac{13}{5}$ by $\frac{1}{- 1}$ .

$y = \frac{13}{5 \cdot - 1} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.4

Multiply $5$ by $- 1$ .

$y = \frac{13}{- 5} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.5

Move the negative in front of the fraction.

$y = - \frac{13}{5} + \frac{\frac{x}{5}}{- 3}$

Step 2.3.3.1.6

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{13}{5} + \frac{x}{5} \cdot \frac{1}{- 3}$

Step 2.3.3.1.7

Move the negative in front of the fraction.

$y = - \frac{13}{5} + \frac{x}{5} (- \frac{1}{3})$

Step 2.3.3.1.8

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

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Step 2.3.3.1.8.1

Multiply $\frac{x}{5}$ by $\frac{1}{3}$ .

$y = - \frac{13}{5} - \frac{x}{5 \cdot 3}$

Step 2.3.3.1.8.2

Multiply $5$ by $3$ .

$y = - \frac{13}{5} - \frac{x}{15}$

Step 2.4

Write in $y = m x + b$ form.

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Step 2.4.1

Reorder $- \frac{13}{5}$ and $- \frac{x}{15}$ .

$y = - \frac{x}{15} - \frac{13}{5}$

Step 2.4.2

Reorder terms.

$y = - (\frac{1}{15} x) - \frac{13}{5}$

Step 2.4.3

Remove parentheses.

$y = - \frac{1}{15} x - \frac{13}{5}$