Algebra Examples

$6 - \frac{5 y + 4 x}{2} = 4$

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 left side.

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Step 2.1.1

Simplify $6 - \frac{5 y + 4 x}{2}$ .

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Step 2.1.1.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 \cdot \frac{2}{2} - \frac{5 y + 4 x}{2} = 4$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Combine $6$ and $\frac{2}{2}$ .

$\frac{6 \cdot 2}{2} - \frac{5 y + 4 x}{2} = 4$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{6 \cdot 2 - (5 y + 4 x)}{2} = 4$

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Multiply $6$ by $2$ .

$\frac{12 - (5 y + 4 x)}{2} = 4$

Step 2.1.1.3.2

Apply the distributive property.

$\frac{12 - (5 y) - (4 x)}{2} = 4$

Step 2.1.1.3.3

Multiply $5$ by $- 1$ .

$\frac{12 - 5 y - (4 x)}{2} = 4$

Step 2.1.1.3.4

Multiply $4$ by $- 1$ .

$\frac{12 - 5 y - 4 x}{2} = 4$

Step 2.2

Multiply both sides by $2$ .

$\frac{12 - 5 y - 4 x}{2} \cdot 2 = 4 \cdot 2$

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $\frac{12 - 5 y - 4 x}{2} \cdot 2$ .

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Step 2.3.1.1.1

Cancel the common factor of $2$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

$\frac{12 - 5 y - 4 x}{2} \cdot 2 = 4 \cdot 2$

Step 2.3.1.1.1.2

Rewrite the expression.

$12 - 5 y - 4 x = 4 \cdot 2$

Step 2.3.1.1.2

Simplify the expression.

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Step 2.3.1.1.2.1

Move $12$ .

$- 5 y - 4 x + 12 = 4 \cdot 2$

Step 2.3.1.1.2.2

Reorder $- 5 y$ and $- 4 x$ .

$- 4 x - 5 y + 12 = 4 \cdot 2$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $4$ by $2$ .

$- 4 x - 5 y + 12 = 8$

Step 2.4

Solve for $y$ .

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Step 2.4.1

Move all terms not containing $y$ to the right side of the equation.

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Step 2.4.1.1

Add $4 x$ to both sides of the equation.

$- 5 y + 12 = 8 + 4 x$

Step 2.4.1.2

Subtract $12$ from both sides of the equation.

$- 5 y = 8 + 4 x - 12$

Step 2.4.1.3

Subtract $12$ from $8$ .

$- 5 y = 4 x - 4$

Step 2.4.2

Divide each term in $- 5 y = 4 x - 4$ by $- 5$ and simplify.

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Step 2.4.2.1

Divide each term in $- 5 y = 4 x - 4$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{4 x}{- 5} + \frac{- 4}{- 5}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $- 5$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{4 x}{- 5} + \frac{- 4}{- 5}$

Step 2.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{- 5} + \frac{- 4}{- 5}$

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Simplify each term.

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Step 2.4.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{4 x}{5} + \frac{- 4}{- 5}$

Step 2.4.2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{4 x}{5} + \frac{4}{5}$

Step 2.5

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

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Step 2.5.1

Reorder terms.

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

Step 2.5.2

Remove parentheses.

$y = - \frac{4}{5} x + \frac{4}{5}$