Pre-Algebra Examples

$(- 4, - 4)$ , $(4, 2)$

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.

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

Step 1.4

Simplify.

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Step 1.4.1

Reduce the expression by cancelling the common factors.

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Step 1.4.1.1

Cancel the common factor of $2 - (- 4)$ and $4 - (- 4)$ .

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Step 1.4.1.1.1

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (- 2) - (- 4)$ .

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

Step 1.4.1.1.3

Reorder terms.

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

Step 1.4.1.1.4

Factor $2$ out of $- 1 (- 2 - 4)$ .

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

Step 1.4.1.1.5

Cancel the common factors.

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Step 1.4.1.1.5.1

Factor $2$ out of $4$ .

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

Step 1.4.1.1.5.2

Factor $2$ out of $- 4 \cdot - 1$ .

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

Step 1.4.1.1.5.3

Factor $2$ out of $2 (2) + 2 (- 2 \cdot - 1)$ .

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

Step 1.4.1.1.5.4

Cancel the common factor.

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

Step 1.4.1.1.5.5

Rewrite the expression.

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

Step 1.4.1.2

Subtract $2$ from $- 1$ .

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 2$ by $- 1$ .

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

Step 1.4.2.2

Add $2$ and $2$ .

$m = \frac{- 1 \cdot - 3}{4}$

Step 1.4.3

Multiply $- 1$ by $- 3$ .

$m = \frac{3}{4}$

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, $y = m x + b$ .

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

Step 2.2

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

$y = (\frac{3}{4}) \cdot (- 4) + b$

Step 2.3

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

$- 4 = (\frac{3}{4}) \cdot (- 4) + b$

Step 2.4

Rewrite the equation as $(\frac{3}{4}) \cdot (- 4) + b = - 4$ .

$(\frac{3}{4}) \cdot (- 4) + b = - 4$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $4$ .

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Step 2.5.1.1

Factor $4$ out of $- 4$ .

$\frac{3}{4} \cdot (4 (- 1)) + b = - 4$

Step 2.5.1.2

Cancel the common factor.

$\frac{3}{4} \cdot (4 \cdot - 1) + b = - 4$

Step 2.5.1.3

Rewrite the expression.

$3 \cdot - 1 + b = - 4$

Step 2.5.2

Multiply $3$ by $- 1$ .

$- 3 + b = - 4$

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 $3$ to both sides of the equation.

$b = - 4 + 3$

Step 2.6.2

Add $- 4$ and $3$ .

$b = - 1$

Step 3

List the slope and y-intercept.

Slope: $\frac{3}{4}$

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

Step 4