Algebra Examples

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

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 $\frac{5}{3}$ and $y$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- (x - 5)$ .

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Step 2.2.1.1

Apply the distributive property.

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

Step 2.2.1.2

Multiply $- 1$ by $- 5$ .

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

Step 2.3

Multiply both sides of the equation by $\frac{3}{5}$ .

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

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $\frac{3}{5} \cdot \frac{5 y}{3}$ .

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Step 2.4.1.1.1

Cancel the common factor of $3$ .

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Step 2.4.1.1.1.1

Cancel the common factor.

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

Step 2.4.1.1.1.2

Rewrite the expression.

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

Step 2.4.1.1.2

Cancel the common factor of $5$ .

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Step 2.4.1.1.2.1

Factor $5$ out of $5 y$ .

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

Step 2.4.1.1.2.2

Cancel the common factor.

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

Step 2.4.1.1.2.3

Rewrite the expression.

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

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

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

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Step 2.4.2.1.1

Apply the distributive property.

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

Step 2.4.2.1.2

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

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

Step 2.4.2.1.3

Cancel the common factor of $5$ .

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Step 2.4.2.1.3.1

Cancel the common factor.

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

Step 2.4.2.1.3.2

Rewrite the expression.

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

Step 2.5

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

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Step 2.5.1

Reorder terms.

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

Step 2.5.2

Remove parentheses.

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