Pre-Algebra Examples

$(\frac{7}{8}, - 4)$ , $(- \frac{1}{4}, - \frac{1}{4})$

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.

$m = \frac{- \frac{1}{4} - (- 4)}{- \frac{1}{4} - (\frac{7}{8})}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply the numerator and denominator of the fraction by $8$ .

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Step 1.4.1.1

Multiply $\frac{- \frac{1}{4} - (- 4)}{- \frac{1}{4} - \frac{7}{8}}$ by $\frac{8}{8}$ .

$m = \frac{8}{8} \cdot \frac{- \frac{1}{4} - (- 4)}{- \frac{1}{4} - \frac{7}{8}}$

Step 1.4.1.2

Combine.

$m = \frac{8 (- \frac{1}{4} - (- 4))}{8 (- \frac{1}{4} - \frac{7}{8})}$

Step 1.4.2

Apply the distributive property.

$m = \frac{8 (- \frac{1}{4}) + 8 (- (- 4))}{8 (- \frac{1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3

Simplify by cancelling.

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Step 1.4.3.1

Cancel the common factor of $4$ .

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Step 1.4.3.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$m = \frac{8 (\frac{- 1}{4}) + 8 (- (- 4))}{8 (- \frac{1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.1.2

Factor $4$ out of $8$ .

$m = \frac{4 (2) (\frac{- 1}{4}) + 8 (- (- 4))}{8 (- \frac{1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.1.3

Cancel the common factor.

$m = \frac{4 \cdot (2 (\frac{- 1}{4})) + 8 (- (- 4))}{8 (- \frac{1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.1.4

Rewrite the expression.

$m = \frac{2 \cdot - 1 + 8 (- (- 4))}{8 (- \frac{1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.2

Multiply $2$ by $- 1$ .

$m = \frac{- 2 + 8 (- (- 4))}{8 (- \frac{1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.3

Cancel the common factor of $4$ .

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Step 1.4.3.3.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$m = \frac{- 2 + 8 (- (- 4))}{8 (\frac{- 1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.3.2

Factor $4$ out of $8$ .

$m = \frac{- 2 + 8 (- (- 4))}{4 (2) (\frac{- 1}{4}) + 8 (- \frac{7}{8})}$

Step 1.4.3.3.3

Cancel the common factor.

$m = \frac{- 2 + 8 (- (- 4))}{4 \cdot (2 (\frac{- 1}{4})) + 8 (- \frac{7}{8})}$

Step 1.4.3.3.4

Rewrite the expression.

$m = \frac{- 2 + 8 (- (- 4))}{2 \cdot - 1 + 8 (- \frac{7}{8})}$

Step 1.4.3.4

Multiply $2$ by $- 1$ .

$m = \frac{- 2 + 8 (- (- 4))}{- 2 + 8 (- \frac{7}{8})}$

Step 1.4.3.5

Cancel the common factor of $8$ .

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Step 1.4.3.5.1

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$m = \frac{- 2 + 8 (- (- 4))}{- 2 + 8 (\frac{- 7}{8})}$

Step 1.4.3.5.2

Cancel the common factor.

$m = \frac{- 2 + 8 (- (- 4))}{- 2 + 8 (\frac{- 7}{8})}$

Step 1.4.3.5.3

Rewrite the expression.

$m = \frac{- 2 + 8 (- (- 4))}{- 2 - 7}$

Step 1.4.4

Simplify the numerator.

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Step 1.4.4.1

Multiply $8 (- (- 4))$ .

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Step 1.4.4.1.1

Multiply $- 1$ by $- 4$ .

$m = \frac{- 2 + 8 \cdot 4}{- 2 - 7}$

Step 1.4.4.1.2

Multiply $8$ by $4$ .

$m = \frac{- 2 + 32}{- 2 - 7}$

Step 1.4.4.2

Add $- 2$ and $32$ .

$m = \frac{30}{- 2 - 7}$

Step 1.4.5

Reduce the expression by cancelling the common factors.

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Step 1.4.5.1

Subtract $7$ from $- 2$ .

$m = \frac{30}{- 9}$

Step 1.4.5.2

Cancel the common factor of $30$ and $- 9$ .

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Step 1.4.5.2.1

Factor $3$ out of $30$ .

$m = \frac{3 (10)}{- 9}$

Step 1.4.5.2.2

Cancel the common factors.

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Step 1.4.5.2.2.1

Factor $3$ out of $- 9$ .

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

Step 1.4.5.2.2.2

Cancel the common factor.

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

Step 1.4.5.2.2.3

Rewrite the expression.

$m = \frac{10}{- 3}$

Step 1.4.5.3

Move the negative in front of the fraction.

$m = - \frac{10}{3}$

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, $y = m x + b$ .

$y = (- \frac{10}{3}) \cdot x + b$

Step 2.2

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

$y = (- \frac{10}{3}) \cdot (\frac{7}{8}) + b$

Step 2.3

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

$- 4 = (- \frac{10}{3}) \cdot (\frac{7}{8}) + b$

Step 2.4

Rewrite the equation as $(- \frac{10}{3}) \cdot (\frac{7}{8}) + b = - 4$ .

$(- \frac{10}{3}) \cdot (\frac{7}{8}) + b = - 4$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $2$ .

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Step 2.5.1.1

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$\frac{- 10}{3} \cdot \frac{7}{8} + b = - 4$

Step 2.5.1.2

Factor $2$ out of $- 10$ .

$\frac{2 (- 5)}{3} \cdot \frac{7}{8} + b = - 4$

Step 2.5.1.3

Factor $2$ out of $8$ .

$\frac{2 \cdot - 5}{3} \cdot \frac{7}{2 \cdot 4} + b = - 4$

Step 2.5.1.4

Cancel the common factor.

$\frac{2 \cdot - 5}{3} \cdot \frac{7}{2 \cdot 4} + b = - 4$

Step 2.5.1.5

Rewrite the expression.

$\frac{- 5}{3} \cdot \frac{7}{4} + b = - 4$

Step 2.5.2

Multiply $\frac{- 5}{3}$ by $\frac{7}{4}$ .

$\frac{- 5 \cdot 7}{3 \cdot 4} + b = - 4$

Step 2.5.3

Multiply $- 5$ by $7$ .

$\frac{- 35}{3 \cdot 4} + b = - 4$

Step 2.5.4

Multiply $3$ by $4$ .

$\frac{- 35}{12} + b = - 4$

Step 2.5.5

Move the negative in front of the fraction.

$- \frac{35}{12} + b = - 4$

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 $\frac{35}{12}$ to both sides of the equation.

$b = - 4 + \frac{35}{12}$

Step 2.6.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$b = - 4 \cdot \frac{12}{12} + \frac{35}{12}$

Step 2.6.3

Combine $- 4$ and $\frac{12}{12}$ .

$b = \frac{- 4 \cdot 12}{12} + \frac{35}{12}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{- 4 \cdot 12 + 35}{12}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $- 4$ by $12$ .

$b = \frac{- 48 + 35}{12}$

Step 2.6.5.2

Add $- 48$ and $35$ .

$b = \frac{- 13}{12}$

Step 2.6.6

Move the negative in front of the fraction.

$b = - \frac{13}{12}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{10}{3}$

y-intercept: $(0, - \frac{13}{12})$

Step 4