Algebra Examples

$5 (y + 2) = 4 (x - 3)$

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

Simplify $5 (y + 2)$ .

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Step 1.2.1.1

Apply the distributive property.

$5 y + 5 \cdot 2 = 4 (x - 3)$

Step 1.2.1.2

Multiply $5$ by $2$ .

$5 y + 10 = 4 (x - 3)$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify $4 (x - 3)$ .

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Step 1.3.1.1

Apply the distributive property.

$5 y + 10 = 4 x + 4 \cdot - 3$

Step 1.3.1.2

Multiply $4$ by $- 3$ .

$5 y + 10 = 4 x - 12$

Step 1.4

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

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Step 1.4.1

Subtract $10$ from both sides of the equation.

$5 y = 4 x - 12 - 10$

Step 1.4.2

Subtract $10$ from $- 12$ .

$5 y = 4 x - 22$

Step 1.5

Divide each term in $5 y = 4 x - 22$ by $5$ and simplify.

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Step 1.5.1

Divide each term in $5 y = 4 x - 22$ by $5$ .

$\frac{5 y}{5} = \frac{4 x}{5} + \frac{- 22}{5}$

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Cancel the common factor of $5$ .

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Step 1.5.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{4 x}{5} + \frac{- 22}{5}$

Step 1.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{5} + \frac{- 22}{5}$

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Move the negative in front of the fraction.

$y = \frac{4 x}{5} - \frac{22}{5}$

Step 1.6

Reorder terms.

$y = \frac{4}{5} x - \frac{22}{5}$

Step 2

Using the slope-intercept form, the slope is $\frac{4}{5}$ .

$m = \frac{4}{5}$

Step 3