Pre-Algebra Examples

(- 3, - 9)

$(- 3, - 9)$ ,

m = 3

$m = 3$

Step 1

Use the slope

3

$3$ and a given point

(- 3, - 9)

$(- 3, - 9)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

Step 2

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

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

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

Step 3

Solve for

y

$y$ .

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Step 3.1

Simplify

3 \cdot (x + 3)

$3 \cdot (x + 3)$ .

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Step 3.1.1

Rewrite.

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

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

Step 3.1.2

Simplify by adding zeros.

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

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

Step 3.1.3

Apply the distributive property.

y + 9 = 3 x + 3 \cdot 3

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

Step 3.1.4

Multiply

3

$3$ by

3

$3$ .

y + 9 = 3 x + 9

$y + 9 = 3 x + 9$

y + 9 = 3 x + 9

$y + 9 = 3 x + 9$

Step 3.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 3.2.1

Subtract

9

$9$ from both sides of the equation.

y = 3 x + 9 - 9

$y = 3 x + 9 - 9$

Step 3.2.2

Combine the opposite terms in

3 x + 9 - 9

$3 x + 9 - 9$ .

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Step 3.2.2.1

Subtract

9

$9$ from

9

$9$ .

y = 3 x + 0

$y = 3 x + 0$

Step 3.2.2.2

Add

3 x

$3 x$ and

0

$0$ .

y = 3 x

$y = 3 x$

y = 3 x

$y = 3 x$

y = 3 x

$y = 3 x$

y = 3 x

$y = 3 x$

Step 4

List the equation in different forms.

Slope-intercept form:

y = 3 x

$y = 3 x$

Point-slope form:

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

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

Step 5

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