Pre-Algebra Examples

$y + 2 = \frac{3}{2} \cdot (x + 7)$

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 right side.

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Step 1.2.1

Simplify $\frac{3}{2} \cdot (x + 7)$ .

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Step 1.2.1.1

Apply the distributive property.

$y + 2 = \frac{3}{2} x + \frac{3}{2} \cdot 7$

Step 1.2.1.2

Combine $\frac{3}{2}$ and $x$ .

$y + 2 = \frac{3 x}{2} + \frac{3}{2} \cdot 7$

Step 1.2.1.3

Multiply $\frac{3}{2} \cdot 7$ .

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Step 1.2.1.3.1

Combine $\frac{3}{2}$ and $7$ .

$y + 2 = \frac{3 x}{2} + \frac{3 \cdot 7}{2}$

Step 1.2.1.3.2

Multiply $3$ by $7$ .

$y + 2 = \frac{3 x}{2} + \frac{21}{2}$

Step 1.3

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

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Step 1.3.1

Subtract $2$ from both sides of the equation.

$y = \frac{3 x}{2} + \frac{21}{2} - 2$

Step 1.3.2

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

$y = \frac{3 x}{2} + \frac{21}{2} - 2 \cdot \frac{2}{2}$

Step 1.3.3

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

$y = \frac{3 x}{2} + \frac{21}{2} + \frac{- 2 \cdot 2}{2}$

Step 1.3.4

Combine the numerators over the common denominator.

$y = \frac{3 x}{2} + \frac{21 - 2 \cdot 2}{2}$

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $- 2$ by $2$ .

$y = \frac{3 x}{2} + \frac{21 - 4}{2}$

Step 1.3.5.2

Subtract $4$ from $21$ .

$y = \frac{3 x}{2} + \frac{17}{2}$

Step 1.4

Reorder terms.

$y = \frac{3}{2} x + \frac{17}{2}$

Step 2

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

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

Step 3