Precalculus Examples

$(- 3, - 9)$ , $m = 3$

Step 1

Use the slope $3$ and a given point $(- 3, - 9)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = 3 \cdot (x - (- 3))$

Step 2

Simplify the equation and keep it in point-slope form.

$y + 9 = 3 \cdot (x + 3)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $3 \cdot (x + 3)$ .

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Step 3.1.1

Rewrite.

$y + 9 = 0 + 0 + 3 \cdot (x + 3)$

Step 3.1.2

Simplify by adding zeros.

$y + 9 = 3 \cdot (x + 3)$

Step 3.1.3

Apply the distributive property.

$y + 9 = 3 x + 3 \cdot 3$

Step 3.1.4

Multiply $3$ by $3$ .

$y + 9 = 3 x + 9$

Step 3.2

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

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Step 3.2.1

Subtract $9$ from both sides of the equation.

$y = 3 x + 9 - 9$

Step 3.2.2

Combine the opposite terms in $3 x + 9 - 9$ .

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Step 3.2.2.1

Subtract $9$ from $9$ .

$y = 3 x + 0$

Step 3.2.2.2

Add $3 x$ and $0$ .

$y = 3 x$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = 3 x$

Point-slope form:

$y + 9 = 3 \cdot (x + 3)$

Step 5

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