Pre-Algebra Examples

$(6, - 3)$ , $(- 12, 3)$

Step 1

Find the value of the slope.

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Step 1.1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 1.2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

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

Step 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{3 - (- 3)}{- 12 - (6)}$

Step 1.4

Simplify.

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Step 1.4.1

Cancel the common factor of $3 - (- 3)$ and $- 12 - (6)$ .

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Step 1.4.1.1

Rewrite $- 12$ as $- 1 (12)$ .

$m = \frac{3 - (- 3)}{- 1 \cdot 12 - (6)}$

Step 1.4.1.2

Factor $- 1$ out of $- 1 (12) - (6)$ .

$m = \frac{3 - (- 3)}{- 1 (12 + 6)}$

Step 1.4.1.3

Reorder terms.

$m = \frac{3 - 3 \cdot - 1}{- 1 (12 + 6)}$

Step 1.4.1.4

Factor $3$ out of $3$ .

$m = \frac{3 (1) - 3 \cdot - 1}{- 1 (12 + 6)}$

Step 1.4.1.5

Factor $3$ out of $- 3 \cdot - 1$ .

$m = \frac{3 (1) + 3 (1)}{- 1 (12 + 6)}$

Step 1.4.1.6

Factor $3$ out of $3 (1) + 3 (- - 1)$ .

$m = \frac{3 (1 + 1)}{- 1 (12 + 6)}$

Step 1.4.1.7

Cancel the common factors.

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Step 1.4.1.7.1

Factor $3$ out of $- 1 (12 + 6)$ .

$m = \frac{3 (1 + 1)}{3 (- 1 (4 + 2))}$

Step 1.4.1.7.2

Cancel the common factor.

$m = \frac{3 (1 + 1)}{3 (- 1 (4 + 2))}$

Step 1.4.1.7.3

Rewrite the expression.

$m = \frac{1 + 1}{- 1 (4 + 2)}$

Step 1.4.2

Simplify the numerator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{1 + 1}{- 1 (4 + 2)}$

Step 1.4.2.2

Add $1$ and $1$ .

$m = \frac{2}{- 1 (4 + 2)}$

Step 1.4.3

Reduce the expression by cancelling the common factors.

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Step 1.4.3.1

Add $4$ and $2$ .

$m = \frac{2}{- 1 \cdot 6}$

Step 1.4.3.2

Multiply $- 1$ by $6$ .

$m = \frac{2}{- 6}$

Step 1.4.3.3

Cancel the common factor of $2$ and $- 6$ .

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Step 1.4.3.3.1

Factor $2$ out of $2$ .

$m = \frac{2 (1)}{- 6}$

Step 1.4.3.3.2

Cancel the common factors.

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Step 1.4.3.3.2.1

Factor $2$ out of $- 6$ .

$m = \frac{2 \cdot 1}{2 \cdot - 3}$

Step 1.4.3.3.2.2

Cancel the common factor.

$m = \frac{2 \cdot 1}{2 \cdot - 3}$

Step 1.4.3.3.2.3

Rewrite the expression.

$m = \frac{1}{- 3}$

Step 1.4.3.4

Move the negative in front of the fraction.

$m = - \frac{1}{3}$

Step 2

Find the value of the y-intercept.

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Step 2.1

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (- \frac{1}{3}) \cdot x + b$

Step 2.2

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (- \frac{1}{3}) \cdot (6) + b$

Step 2.3

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$- 3 = (- \frac{1}{3}) \cdot (6) + b$

Step 2.4

Rewrite the equation as $(- \frac{1}{3}) \cdot (6) + b = - 3$ .

$(- \frac{1}{3}) \cdot (6) + b = - 3$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $3$ .

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Step 2.5.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{- 1}{3} \cdot 6 + b = - 3$

Step 2.5.1.2

Factor $3$ out of $6$ .

$\frac{- 1}{3} \cdot (3 (2)) + b = - 3$

Step 2.5.1.3

Cancel the common factor.

$\frac{- 1}{3} \cdot (3 \cdot 2) + b = - 3$

Step 2.5.1.4

Rewrite the expression.

$- 1 \cdot 2 + b = - 3$

Step 2.5.2

Multiply $- 1$ by $2$ .

$- 2 + b = - 3$

Step 2.6

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

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Step 2.6.1

Add $2$ to both sides of the equation.

$b = - 3 + 2$

Step 2.6.2

Add $- 3$ and $2$ .

$b = - 1$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{3}$

y-intercept: $(0, - 1)$

Step 4