Pre-Algebra Examples

$(0, 26)$ , $(10, 8)$

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.

$m = \frac{8 - (26)}{10 - (0)}$

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 $26$ .

$m = \frac{8 - 26}{10 - (0)}$

Step 1.4.1.2

Subtract $26$ from $8$ .

$m = \frac{- 18}{10 - (0)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $0$ .

$m = \frac{- 18}{10 + 0}$

Step 1.4.2.2

Add $10$ and $0$ .

$m = \frac{- 18}{10}$

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 $- 18$ and $10$ .

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Step 1.4.3.1.1

Factor $2$ out of $- 18$ .

$m = \frac{2 (- 9)}{10}$

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 $10$ .

$m = \frac{2 \cdot - 9}{2 \cdot 5}$

Step 1.4.3.1.2.2

Cancel the common factor.

$m = \frac{2 \cdot - 9}{2 \cdot 5}$

Step 1.4.3.1.2.3

Rewrite the expression.

$m = \frac{- 9}{5}$

Step 1.4.3.2

Move the negative in front of the fraction.

$m = - \frac{9}{5}$

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, $y = m x + b$ .

$y = (- \frac{9}{5}) \cdot x + b$

Step 2.2

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

$y = (- \frac{9}{5}) \cdot (0) + b$

Step 2.3

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

$26 = (- \frac{9}{5}) \cdot (0) + b$

Step 2.4

Rewrite the equation as $(- \frac{9}{5}) \cdot (0) + b = 26$ .

$(- \frac{9}{5}) \cdot (0) + b = 26$

Step 2.5

Simplify $(- \frac{9}{5}) \cdot (0) + b$ .

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Step 2.5.1

Multiply $(- \frac{9}{5}) (0)$ .

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Step 2.5.1.1

Multiply $0$ by $- 1$ .

$0 (\frac{9}{5}) + b = 26$

Step 2.5.1.2

Multiply $0$ by $\frac{9}{5}$ .

$0 + b = 26$

Step 2.5.2

Add $0$ and $b$ .

$b = 26$

Step 3

List the slope and y-intercept.

Slope: $- \frac{9}{5}$

y-intercept: $(0, 26)$

Step 4