Algebra Examples

$3 (y - 1) = 2 x + 2$

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 $3 (y - 1)$ .

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Step 1.2.1.1

Apply the distributive property.

$3 y + 3 \cdot - 1 = 2 x + 2$

Step 1.2.1.2

Multiply $3$ by $- 1$ .

$3 y - 3 = 2 x + 2$

Step 1.3

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

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Step 1.3.1

Add $3$ to both sides of the equation.

$3 y = 2 x + 2 + 3$

Step 1.3.2

Add $2$ and $3$ .

$3 y = 2 x + 5$

Step 1.4

Divide each term in $3 y = 2 x + 5$ by $3$ and simplify.

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Step 1.4.1

Divide each term in $3 y = 2 x + 5$ by $3$ .

$\frac{3 y}{3} = \frac{2 x}{3} + \frac{5}{3}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $3$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{2 x}{3} + \frac{5}{3}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 x}{3} + \frac{5}{3}$

Step 1.5

Reorder terms.

$y = \frac{2}{3} x + \frac{5}{3}$

Step 2

Using the slope-intercept form, the slope is $\frac{2}{3}$ .

$m = \frac{2}{3}$

Step 3