Pre-Algebra Examples

$(0, 0)$ , $(- \frac{1}{8}, \frac{1}{9})$

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.

$m = \frac{\frac{1}{9} - (0)}{- \frac{1}{8} - (0)}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply the numerator and denominator of the fraction by $72$ .

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Step 1.4.1.1

Multiply $\frac{\frac{1}{9} - (0)}{- \frac{1}{8} - (0)}$ by $\frac{72}{72}$ .

$m = \frac{72}{72} \cdot \frac{\frac{1}{9} - (0)}{- \frac{1}{8} - (0)}$

Step 1.4.1.2

Combine.

$m = \frac{72 (\frac{1}{9} - (0))}{72 (- \frac{1}{8} - (0))}$

Step 1.4.2

Apply the distributive property.

$m = \frac{72 (\frac{1}{9}) + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Step 1.4.3

Simplify by cancelling.

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Step 1.4.3.1

Cancel the common factor of $9$ .

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Step 1.4.3.1.1

Factor $9$ out of $72$ .

$m = \frac{9 (8) (\frac{1}{9}) + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Step 1.4.3.1.2

Cancel the common factor.

$m = \frac{9 \cdot (8 (\frac{1}{9})) + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Step 1.4.3.1.3

Rewrite the expression.

$m = \frac{8 + 72 (- (0))}{72 (- \frac{1}{8}) + 72 (- (0))}$

Step 1.4.3.2

Cancel the common factor of $8$ .

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Step 1.4.3.2.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$m = \frac{8 + 72 (- (0))}{72 (\frac{- 1}{8}) + 72 (- (0))}$

Step 1.4.3.2.2

Factor $8$ out of $72$ .

$m = \frac{8 + 72 (- (0))}{8 (9) (\frac{- 1}{8}) + 72 (- (0))}$

Step 1.4.3.2.3

Cancel the common factor.

$m = \frac{8 + 72 (- (0))}{8 \cdot (9 (\frac{- 1}{8})) + 72 (- (0))}$

Step 1.4.3.2.4

Rewrite the expression.

$m = \frac{8 + 72 (- (0))}{9 \cdot - 1 + 72 (- (0))}$

Step 1.4.3.3

Multiply $9$ by $- 1$ .

$m = \frac{8 + 72 (- (0))}{- 9 + 72 (- (0))}$

Step 1.4.4

Simplify the numerator.

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Step 1.4.4.1

Multiply $72 (- (0))$ .

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Step 1.4.4.1.1

Multiply $- 1$ by $0$ .

$m = \frac{8 + 72 \cdot 0}{- 9 + 72 (- (0))}$

Step 1.4.4.1.2

Multiply $72$ by $0$ .

$m = \frac{8 + 0}{- 9 + 72 (- (0))}$

Step 1.4.4.2

Add $8$ and $0$ .

$m = \frac{8}{- 9 + 72 (- (0))}$

Step 1.4.5

Simplify the denominator.

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Step 1.4.5.1

Multiply $72 (- (0))$ .

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Step 1.4.5.1.1

Multiply $- 1$ by $0$ .

$m = \frac{8}{- 9 + 72 \cdot 0}$

Step 1.4.5.1.2

Multiply $72$ by $0$ .

$m = \frac{8}{- 9 + 0}$

Step 1.4.5.2

Add $- 9$ and $0$ .

$m = \frac{8}{- 9}$

Step 1.4.6

Move the negative in front of the fraction.

$m = - \frac{8}{9}$

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, $y = m x + b$ .

$y = (- \frac{8}{9}) \cdot x + b$

Step 2.2

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

$y = (- \frac{8}{9}) \cdot (0) + b$

Step 2.3

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

$0 = (- \frac{8}{9}) \cdot (0) + b$

Step 2.4

Rewrite the equation as $(- \frac{8}{9}) \cdot (0) + b = 0$ .

$(- \frac{8}{9}) \cdot (0) + b = 0$

Step 2.5

Simplify $(- \frac{8}{9}) \cdot (0) + b$ .

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Step 2.5.1

Multiply $(- \frac{8}{9}) (0)$ .

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Step 2.5.1.1

Multiply $0$ by $- 1$ .

$0 (\frac{8}{9}) + b = 0$

Step 2.5.1.2

Multiply $0$ by $\frac{8}{9}$ .

$0 + b = 0$

Step 2.5.2

Add $0$ and $b$ .

$b = 0$

Step 3

List the slope and y-intercept.

Slope: $- \frac{8}{9}$

y-intercept: $(0, 0)$

Step 4