Precalculus Examples

$(y - 3) = \frac{2}{3} \cdot (x + 6)$

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 right side.

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Step 2.1.1

Simplify $\frac{2}{3} \cdot (x + 6)$ .

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Step 2.1.1.1

Apply the distributive property.

$(y - 3) = \frac{2}{3} x + \frac{2}{3} \cdot 6$

Step 2.1.1.2

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

$(y - 3) = \frac{2 x}{3} + \frac{2}{3} \cdot 6$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $6$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Multiply $2$ by $2$ .

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

Step 2.2

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

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Step 2.2.1

Add $3$ to both sides of the equation.

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

Step 2.2.2

Add $4$ and $3$ .

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

Step 2.3

Reorder terms.

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