Finite Math Examples

$(- 48, 0)$ , $(0, - 8)$

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.

$m = \frac{- 8 - (0)}{0 - (- 48)}$

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 $- 8 - (0)$ and $0 - (- 48)$ .

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Step 5.1.1.1

Rewrite $- 8$ as $- 1 (8)$ .

$m = \frac{- 1 \cdot 8 - (0)}{0 - (- 48)}$

Step 5.1.1.2

Factor $- 1$ out of $- 1 (8) - (0)$ .

$m = \frac{- 1 (8 + 0)}{0 - (- 48)}$

Step 5.1.1.3

Reorder terms.

$m = \frac{- 1 (8 + 0)}{0 - 48 \cdot - 1}$

Step 5.1.1.4

Factor $8$ out of $- 1 (8 + 0)$ .

$m = \frac{8 (- 1 (1 + 0))}{0 - 48 \cdot - 1}$

Step 5.1.1.5

Cancel the common factors.

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Step 5.1.1.5.1

Factor $8$ out of $0$ .

$m = \frac{8 (- 1 (1 + 0))}{8 (0) - 48 \cdot - 1}$

Step 5.1.1.5.2

Factor $8$ out of $- 48 \cdot - 1$ .

$m = \frac{8 (- 1 (1 + 0))}{8 (0) + 8 (- 6 \cdot - 1)}$

Step 5.1.1.5.3

Factor $8$ out of $8 (0) + 8 (- 6 \cdot - 1)$ .

$m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}$

Step 5.1.1.5.4

Cancel the common factor.

$m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}$

Step 5.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}$

Step 5.1.2

Add $1$ and $0$ .

$m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 6$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{0 + 6}$

Step 5.2.2

Add $0$ and $6$ .

$m = \frac{- 1 \cdot 1}{6}$

Step 5.3

Simplify the expression.

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Step 5.3.1

Multiply $- 1$ by $1$ .

$m = \frac{- 1}{6}$

Step 5.3.2

Move the negative in front of the fraction.

$m = - \frac{1}{6}$

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.

$y = (- \frac{1}{6}) \cdot x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (- \frac{1}{6}) \cdot (- 48) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$0 = (- \frac{1}{6}) \cdot (- 48) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $- \frac{1}{6} \cdot - 48 + b = 0$ .

$- \frac{1}{6} \cdot - 48 + b = 0$

Step 6.5.2

Simplify each term.

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Step 6.5.2.1

Cancel the common factor of $6$ .

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Step 6.5.2.1.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{- 1}{6} \cdot - 48 + b = 0$

Step 6.5.2.1.2

Factor $6$ out of $- 48$ .

$\frac{- 1}{6} \cdot (6 (- 8)) + b = 0$

Step 6.5.2.1.3

Cancel the common factor.

$\frac{- 1}{6} \cdot (6 \cdot - 8) + b = 0$

Step 6.5.2.1.4

Rewrite the expression.

$- 1 \cdot - 8 + b = 0$

Step 6.5.2.2

Multiply $- 1$ by $- 8$ .

$8 + b = 0$

Step 6.5.3

Subtract $8$ from both sides of the equation.

$b = - 8$

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.

$y = - \frac{1}{6} x - 8$

Step 8