Pre-Algebra Examples

$(- 5, 1)$ , $(5, - 1)$

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.

$m = \frac{- 1 - (1)}{5 - (- 5)}$

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 $1$ .

$m = \frac{- 1 - 1}{5 - (- 5)}$

Step 1.4.1.2

Subtract $1$ from $- 1$ .

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 5$ .

$m = \frac{- 2}{5 + 5}$

Step 1.4.2.2

Add $5$ and $5$ .

$m = \frac{- 2}{10}$

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 $- 2$ and $10$ .

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Step 1.4.3.1.1

Factor $2$ out of $- 2$ .

$m = \frac{2 (- 1)}{10}$

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 $10$ .

$m = \frac{2 \cdot - 1}{2 \cdot 5}$

Step 1.4.3.1.2.2

Cancel the common factor.

$m = \frac{2 \cdot - 1}{2 \cdot 5}$

Step 1.4.3.1.2.3

Rewrite the expression.

$m = \frac{- 1}{5}$

Step 1.4.3.2

Move the negative in front of the fraction.

$m = - \frac{1}{5}$

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, $y = m x + b$ .

$y = (- \frac{1}{5}) \cdot x + b$

Step 2.2

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

$y = (- \frac{1}{5}) \cdot (- 5) + b$

Step 2.3

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

$1 = (- \frac{1}{5}) \cdot (- 5) + b$

Step 2.4

Rewrite the equation as $(- \frac{1}{5}) \cdot (- 5) + b = 1$ .

$(- \frac{1}{5}) \cdot (- 5) + b = 1$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $5$ .

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Step 2.5.1.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{- 1}{5} \cdot - 5 + b = 1$

Step 2.5.1.2

Factor $5$ out of $- 5$ .

$\frac{- 1}{5} \cdot (5 (- 1)) + b = 1$

Step 2.5.1.3

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 \cdot - 1) + b = 1$

Step 2.5.1.4

Rewrite the expression.

$- 1 \cdot - 1 + b = 1$

Step 2.5.2

Multiply $- 1$ by $- 1$ .

$1 + b = 1$

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 $1$ from both sides of the equation.

$b = 1 - 1$

Step 2.6.2

Subtract $1$ from $1$ .

$b = 0$

Step 3

List the slope and y-intercept.

Slope: $- \frac{1}{5}$

y-intercept: $(0, 0)$

Step 4