Pre-Algebra Examples

$(- 3, 2)$ , $(5, - 4)$

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.

$m = \frac{- 4 - (2)}{5 - (- 3)}$

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 $2$ .

$m = \frac{- 4 - 2}{5 - (- 3)}$

Step 1.4.1.2

Subtract $2$ from $- 4$ .

$m = \frac{- 6}{5 - (- 3)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 3$ .

$m = \frac{- 6}{5 + 3}$

Step 1.4.2.2

Add $5$ and $3$ .

$m = \frac{- 6}{8}$

Step 1.4.3

Reduce the expression by cancelling the common factors.

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Step 1.4.3.1

Cancel the common factor of $- 6$ and $8$ .

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Step 1.4.3.1.1

Factor $2$ out of $- 6$ .

$m = \frac{2 (- 3)}{8}$

Step 1.4.3.1.2

Cancel the common factors.

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Step 1.4.3.1.2.1

Factor $2$ out of $8$ .

$m = \frac{2 \cdot - 3}{2 \cdot 4}$

Step 1.4.3.1.2.2

Cancel the common factor.

$m = \frac{2 \cdot - 3}{2 \cdot 4}$

Step 1.4.3.1.2.3

Rewrite the expression.

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

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, $y = m x + b$ .

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

Step 2.3

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

$2 = (- \frac{3}{4}) \cdot (- 3) + b$

Step 2.4

Rewrite the equation as $(- \frac{3}{4}) \cdot (- 3) + b = 2$ .

$(- \frac{3}{4}) \cdot (- 3) + b = 2$

Step 2.5

Multiply $(- \frac{3}{4}) (- 3)$ .

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Step 2.5.1

Multiply $- 3$ by $- 1$ .

$3 (\frac{3}{4}) + b = 2$

Step 2.5.2

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

$\frac{3 \cdot 3}{4} + b = 2$

Step 2.5.3

Multiply $3$ by $3$ .

$\frac{9}{4} + b = 2$

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 $\frac{9}{4}$ from both sides of the equation.

$b = 2 - \frac{9}{4}$

Step 2.6.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$b = 2 \cdot \frac{4}{4} - \frac{9}{4}$

Step 2.6.3

Combine $2$ and $\frac{4}{4}$ .

$b = \frac{2 \cdot 4}{4} - \frac{9}{4}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{2 \cdot 4 - 9}{4}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $2$ by $4$ .

$b = \frac{8 - 9}{4}$

Step 2.6.5.2

Subtract $9$ from $8$ .

$b = \frac{- 1}{4}$

Step 2.6.6

Move the negative in front of the fraction.

$b = - \frac{1}{4}$

Step 3

List the slope and y-intercept.

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

y-intercept: $(0, - \frac{1}{4})$

Step 4