Precalculus Examples

$(- 5, 0)$ , $(5, 0)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

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 3

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 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{0 - (0)}{5 - (- 5)}$

Step 5

Finding the slope $m$ .

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Step 5.1

Reduce the expression by cancelling the common factors.

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Step 5.1.1

Cancel the common factor of $0 - (0)$ and $5 - (- 5)$ .

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Step 5.1.1.1

Rewrite $0$ as $- 1 (0)$ .

$m = \frac{- 1 \cdot 0 - (0)}{5 - (- 5)}$

Step 5.1.1.2

Factor $- 1$ out of $- 1 (0) - (0)$ .

$m = \frac{- 1 (0 + 0)}{5 - (- 5)}$

Step 5.1.1.3

Reorder terms.

$m = \frac{- 1 (0 + 0)}{5 - 5 \cdot - 1}$

Step 5.1.1.4

Factor $5$ out of $- 1 (0 + 0)$ .

$m = \frac{5 (- 1 (0 + 0))}{5 - 5 \cdot - 1}$

Step 5.1.1.5

Cancel the common factors.

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Step 5.1.1.5.1

Factor $5$ out of $5$ .

$m = \frac{5 (- 1 (0 + 0))}{5 (1) - 5 \cdot - 1}$

Step 5.1.1.5.2

Factor $5$ out of $- 5 \cdot - 1$ .

$m = \frac{5 (- 1 (0 + 0))}{5 (1) + 5 (1)}$

Step 5.1.1.5.3

Factor $5$ out of $5 (1) + 5 (- - 1)$ .

$m = \frac{5 (- 1 (0 + 0))}{5 (1 + 1)}$

Step 5.1.1.5.4

Cancel the common factor.

$m = \frac{5 (- 1 (0 + 0))}{5 (1 + 1)}$

Step 5.1.1.5.5

Rewrite the expression.

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

Step 5.1.2

Add $0$ and $0$ .

$m = \frac{- 1 \cdot 0}{1 + 1}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 1 \cdot 0}{1 + 1}$

Step 5.2.2

Add $1$ and $1$ .

$m = \frac{- 1 \cdot 0}{2}$

Step 5.3

Simplify the expression.

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Step 5.3.1

Multiply $- 1$ by $0$ .

$m = \frac{0}{2}$

Step 5.3.2

Divide $0$ by $2$ .

$m = 0$

Step 6

Find the value of $b$ using the formula for the equation of a line.

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Step 6.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 6.2

Substitute the value of $m$ into the equation.

$y = (0) \cdot x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (0) \cdot (- 5) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$0 = (0) \cdot (- 5) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $(0) \cdot (- 5) + b = 0$ .

$(0) \cdot (- 5) + b = 0$

Step 6.5.2

Simplify $(0) \cdot (- 5) + b$ .

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Step 6.5.2.1

Multiply $0$ by $- 5$ .

$0 + b = 0$

Step 6.5.2.2

Add $0$ and $b$ .

$b = 0$

Step 7

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = 0$

Step 8