Pre-Algebra Examples

$(- 20, - 4)$ , $(- 12, - 10)$

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.

$m = \frac{- 10 - (- 4)}{- 12 - (- 20)}$

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 $- 10 - (- 4)$ and $- 12 - (- 20)$ .

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Step 1.4.1.1.1

Rewrite $- 10$ as $- 1 (10)$ .

$m = \frac{- 1 \cdot 10 - (- 4)}{- 12 - (- 20)}$

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (10) - (- 4)$ .

$m = \frac{- 1 (10 - 4)}{- 12 - (- 20)}$

Step 1.4.1.1.3

Reorder terms.

$m = \frac{- 1 (10 - 4)}{- 12 - 20 \cdot - 1}$

Step 1.4.1.1.4

Factor $2$ out of $- 1 (10 - 4)$ .

$m = \frac{2 (- 1 (5 - 2))}{- 12 - 20 \cdot - 1}$

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 $- 12$ .

$m = \frac{2 (- 1 (5 - 2))}{2 (- 6) - 20 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $2$ out of $- 20 \cdot - 1$ .

$m = \frac{2 (- 1 (5 - 2))}{2 (- 6) + 2 (- 10 \cdot - 1)}$

Step 1.4.1.1.5.3

Factor $2$ out of $2 (- 6) + 2 (- 10 \cdot - 1)$ .

$m = \frac{2 (- 1 (5 - 2))}{2 (- 6 - 10 \cdot - 1)}$

Step 1.4.1.1.5.4

Cancel the common factor.

$m = \frac{2 (- 1 (5 - 2))}{2 (- 6 - 10 \cdot - 1)}$

Step 1.4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (5 - 2)}{- 6 - 10 \cdot - 1}$

Step 1.4.1.2

Subtract $2$ from $5$ .

$m = \frac{- 1 \cdot 3}{- 6 - 10 \cdot - 1}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 10$ by $- 1$ .

$m = \frac{- 1 \cdot 3}{- 6 + 10}$

Step 1.4.2.2

Add $- 6$ and $10$ .

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

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Multiply $- 1$ by $3$ .

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

Step 1.4.3.2

Move the negative in front of the fraction.

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

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, $y = m x + b$ .

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

Step 2.2

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

$y = (- \frac{3}{4}) \cdot (- 20) + b$

Step 2.3

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

$- 4 = (- \frac{3}{4}) \cdot (- 20) + b$

Step 2.4

Rewrite the equation as $(- \frac{3}{4}) \cdot (- 20) + b = - 4$ .

$(- \frac{3}{4}) \cdot (- 20) + b = - 4$

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

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot - 20 + b = - 4$

Step 2.5.1.2

Factor $4$ out of $- 20$ .

$\frac{- 3}{4} \cdot (4 (- 5)) + b = - 4$

Step 2.5.1.3

Cancel the common factor.

$\frac{- 3}{4} \cdot (4 \cdot - 5) + b = - 4$

Step 2.5.1.4

Rewrite the expression.

$- 3 \cdot - 5 + b = - 4$

Step 2.5.2

Multiply $- 3$ by $- 5$ .

$15 + b = - 4$

Step 2.6

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

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Step 2.6.1

Subtract $15$ from both sides of the equation.

$b = - 4 - 15$

Step 2.6.2

Subtract $15$ from $- 4$ .

$b = - 19$

Step 3

List the slope and y-intercept.

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

y-intercept: $(0, - 19)$

Step 4