Pre-Algebra Examples

$\frac{4}{5} y = - \frac{11}{6} x$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Simplify the left side.

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Step 1.2.1

Combine $\frac{4}{5}$ and $y$ .

$\frac{4 y}{5} = - \frac{11}{6} x$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify $- \frac{11}{6} x$ .

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Step 1.3.1.1

Combine $x$ and $\frac{11}{6}$ .

$\frac{4 y}{5} = - \frac{x \cdot 11}{6}$

Step 1.3.1.2

Move $11$ to the left of $x$ .

$\frac{4 y}{5} = - \frac{11 x}{6}$

Step 1.4

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 y}{5} = \frac{5}{4} (- \frac{11 x}{6})$

Step 1.5

Simplify both sides of the equation.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Simplify $\frac{5}{4} \cdot \frac{4 y}{5}$ .

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Step 1.5.1.1.1

Cancel the common factor of $5$ .

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Step 1.5.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 y}{5} = \frac{5}{4} (- \frac{11 x}{6})$

Step 1.5.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{5}{4} (- \frac{11 x}{6})$

Step 1.5.1.1.2

Cancel the common factor of $4$ .

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Step 1.5.1.1.2.1

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{5}{4} (- \frac{11 x}{6})$

Step 1.5.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{5}{4} (- \frac{11 x}{6})$

Step 1.5.1.1.2.3

Rewrite the expression.

$y = \frac{5}{4} (- \frac{11 x}{6})$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Multiply $\frac{5}{4} (- \frac{11 x}{6})$ .

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Step 1.5.2.1.1

Multiply $\frac{5}{4}$ by $\frac{11 x}{6}$ .

$y = - \frac{5 (11 x)}{4 \cdot 6}$

Step 1.5.2.1.2

Multiply $11$ by $5$ .

$y = - \frac{55 x}{4 \cdot 6}$

Step 1.5.2.1.3

Multiply $4$ by $6$ .

$y = - \frac{55 x}{24}$

Step 1.6

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

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Step 1.6.1

Reorder terms.

$y = - (\frac{55}{24} x)$

Step 1.6.2

Remove parentheses.

$y = - \frac{55}{24} x$

Step 2

Using the slope-intercept form, the slope is $- \frac{55}{24}$ .

$m = - \frac{55}{24}$

Step 3