Algebra Examples

$2 - (5 y + 2 x) = 8 (x - y)$

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

Apply the distributive property.

$2 - (5 y) - (2 x) = 8 (x - y)$

Step 2.1.1.2

Multiply $5$ by $- 1$ .

$2 - 5 y - (2 x) = 8 (x - y)$

Step 2.1.1.3

Multiply $2$ by $- 1$ .

$2 - 5 y - 2 x = 8 (x - y)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $8 (x - y)$ .

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Step 2.2.1.1

Apply the distributive property.

$2 - 5 y - 2 x = 8 x + 8 (- y)$

Step 2.2.1.2

Multiply $- 1$ by $8$ .

$2 - 5 y - 2 x = 8 x - 8 y$

Step 2.3

Move all terms containing $y$ to the left side of the equation.

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Step 2.3.1

Add $8 y$ to both sides of the equation.

$2 - 5 y - 2 x + 8 y = 8 x$

Step 2.3.2

Add $- 5 y$ and $8 y$ .

$2 - 2 x + 3 y = 8 x$

Step 2.4

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

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Step 2.4.1

Subtract $2$ from both sides of the equation.

$- 2 x + 3 y = 8 x - 2$

Step 2.4.2

Add $2 x$ to both sides of the equation.

$3 y = 8 x - 2 + 2 x$

Step 2.4.3

Add $8 x$ and $2 x$ .

$3 y = 10 x - 2$

Step 2.5

Divide each term in $3 y = 10 x - 2$ by $3$ and simplify.

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Step 2.5.1

Divide each term in $3 y = 10 x - 2$ by $3$ .

$\frac{3 y}{3} = \frac{10 x}{3} + \frac{- 2}{3}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $3$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{10 x}{3} + \frac{- 2}{3}$

Step 2.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{10 x}{3} + \frac{- 2}{3}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Move the negative in front of the fraction.

$y = \frac{10 x}{3} - \frac{2}{3}$

Step 2.6

Reorder terms.

$y = \frac{10}{3} x - \frac{2}{3}$