Pre-Algebra Examples

$(3, - 5)$ , $(- 9, - 8)$

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.

$m = \frac{- 8 - (- 5)}{- 9 - (3)}$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $- 5$ .

$m = \frac{- 8 + 5}{- 9 - (3)}$

Step 1.4.1.2

Add $- 8$ and $5$ .

$m = \frac{- 3}{- 9 - (3)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $3$ .

$m = \frac{- 3}{- 9 - 3}$

Step 1.4.2.2

Subtract $3$ from $- 9$ .

$m = \frac{- 3}{- 12}$

Step 1.4.3

Cancel the common factor of $- 3$ and $- 12$ .

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Step 1.4.3.1

Factor $- 3$ out of $- 3$ .

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

Step 1.4.3.2

Cancel the common factors.

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Step 1.4.3.2.1

Factor $- 3$ out of $- 12$ .

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

Step 1.4.3.2.2

Cancel the common factor.

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

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{1}{4}$

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, $y = m x + b$ .

$y = (\frac{1}{4}) x + b$

Step 2.2

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

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

Step 2.3

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

$- 5 = (\frac{1}{4}) \cdot (3) + b$

Step 2.4

Rewrite the equation as $(\frac{1}{4}) \cdot (3) + b = - 5$ .

$(\frac{1}{4}) \cdot (3) + b = - 5$

Step 2.5

Combine $\frac{1}{4}$ and $3$ .

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

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 $\frac{3}{4}$ from both sides of the equation.

$b = - 5 - \frac{3}{4}$

Step 2.6.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.6.3

Combine $- 5$ and $\frac{4}{4}$ .

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

Step 2.6.4

Combine the numerators over the common denominator.

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

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $- 5$ by $4$ .

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

Step 2.6.5.2

Subtract $3$ from $- 20$ .

$b = \frac{- 23}{4}$

Step 2.6.6

Move the negative in front of the fraction.

$b = - \frac{23}{4}$

Step 3

List the slope and y-intercept.

Slope: $\frac{1}{4}$

y-intercept: $(0, - \frac{23}{4})$

Step 4