Pre-Algebra Examples

$(\frac{8}{5}, \frac{3}{5})$ , $(- \frac{4}{5}, \frac{11}{5})$

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.

$m = \frac{\frac{11}{5} - (\frac{3}{5})}{- \frac{4}{5} - (\frac{8}{5})}$

Step 1.4

Simplify.

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Step 1.4.1

Multiply the numerator and denominator of the fraction by $5$ .

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Step 1.4.1.1

Multiply $\frac{\frac{11}{5} - \frac{3}{5}}{- \frac{4}{5} - \frac{8}{5}}$ by $\frac{5}{5}$ .

$m = \frac{5}{5} \cdot \frac{\frac{11}{5} - \frac{3}{5}}{- \frac{4}{5} - \frac{8}{5}}$

Step 1.4.1.2

Combine.

$m = \frac{5 (\frac{11}{5} - \frac{3}{5})}{5 (- \frac{4}{5} - \frac{8}{5})}$

Step 1.4.2

Apply the distributive property.

$m = \frac{5 (\frac{11}{5}) + 5 (- \frac{3}{5})}{5 (- \frac{4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3

Simplify by cancelling.

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Step 1.4.3.1

Cancel the common factor of $5$ .

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Step 1.4.3.1.1

Cancel the common factor.

$m = \frac{5 (\frac{11}{5}) + 5 (- \frac{3}{5})}{5 (- \frac{4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.1.2

Rewrite the expression.

$m = \frac{11 + 5 (- \frac{3}{5})}{5 (- \frac{4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.2

Cancel the common factor of $5$ .

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Step 1.4.3.2.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$m = \frac{11 + 5 (\frac{- 3}{5})}{5 (- \frac{4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.2.2

Cancel the common factor.

$m = \frac{11 + 5 (\frac{- 3}{5})}{5 (- \frac{4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{11 - 3}{5 (- \frac{4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.3

Cancel the common factor of $5$ .

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Step 1.4.3.3.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$m = \frac{11 - 3}{5 (\frac{- 4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.3.2

Cancel the common factor.

$m = \frac{11 - 3}{5 (\frac{- 4}{5}) + 5 (- \frac{8}{5})}$

Step 1.4.3.3.3

Rewrite the expression.

$m = \frac{11 - 3}{- 4 + 5 (- \frac{8}{5})}$

Step 1.4.3.4

Cancel the common factor of $5$ .

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Step 1.4.3.4.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$m = \frac{11 - 3}{- 4 + 5 (\frac{- 8}{5})}$

Step 1.4.3.4.2

Cancel the common factor.

$m = \frac{11 - 3}{- 4 + 5 (\frac{- 8}{5})}$

Step 1.4.3.4.3

Rewrite the expression.

$m = \frac{11 - 3}{- 4 - 8}$

Step 1.4.4

Reduce the expression by cancelling the common factors.

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Step 1.4.4.1

Subtract $3$ from $11$ .

$m = \frac{8}{- 4 - 8}$

Step 1.4.4.2

Subtract $8$ from $- 4$ .

$m = \frac{8}{- 12}$

Step 1.4.4.3

Cancel the common factor of $8$ and $- 12$ .

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Step 1.4.4.3.1

Factor $4$ out of $8$ .

$m = \frac{4 (2)}{- 12}$

Step 1.4.4.3.2

Cancel the common factors.

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Step 1.4.4.3.2.1

Factor $4$ out of $- 12$ .

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

Step 1.4.4.3.2.2

Cancel the common factor.

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

Step 1.4.4.3.2.3

Rewrite the expression.

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

Step 1.4.4.4

Move the negative in front of the fraction.

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

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, $y = m x + b$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Rewrite the equation as $(- \frac{2}{3}) \cdot (\frac{8}{5}) + b = \frac{3}{5}$ .

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

Step 2.5

Multiply $(- \frac{2}{3}) (\frac{8}{5})$ .

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Step 2.5.1

Multiply $\frac{8}{5}$ by $\frac{2}{3}$ .

$- \frac{8 \cdot 2}{5 \cdot 3} + b = \frac{3}{5}$

Step 2.5.2

Multiply $8$ by $2$ .

$- \frac{16}{5 \cdot 3} + b = \frac{3}{5}$

Step 2.5.3

Multiply $5$ by $3$ .

$- \frac{16}{15} + b = \frac{3}{5}$

Step 2.6

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

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Step 2.6.1

Add $\frac{16}{15}$ to both sides of the equation.

$b = \frac{3}{5} + \frac{16}{15}$

Step 2.6.2

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = \frac{3}{5} \cdot \frac{3}{3} + \frac{16}{15}$

Step 2.6.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.3.1

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$b = \frac{3 \cdot 3}{5 \cdot 3} + \frac{16}{15}$

Step 2.6.3.2

Multiply $5$ by $3$ .

$b = \frac{3 \cdot 3}{15} + \frac{16}{15}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{3 \cdot 3 + 16}{15}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $3$ by $3$ .

$b = \frac{9 + 16}{15}$

Step 2.6.5.2

Add $9$ and $16$ .

$b = \frac{25}{15}$

Step 2.6.6

Cancel the common factor of $25$ and $15$ .

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Step 2.6.6.1

Factor $5$ out of $25$ .

$b = \frac{5 (5)}{15}$

Step 2.6.6.2

Cancel the common factors.

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Step 2.6.6.2.1

Factor $5$ out of $15$ .

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

Step 2.6.6.2.2

Cancel the common factor.

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

Step 2.6.6.2.3

Rewrite the expression.

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

Step 3

List the slope and y-intercept.

Slope: $- \frac{2}{3}$

y-intercept: $(0, \frac{5}{3})$

Step 4