Finite Math Examples

$(- 16, 0)$ , $(0, - 4)$

Step 1

Find the slope of the line between $(- 16, 0)$ and $(0, - 4)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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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.

$m = \frac{- 4 - (0)}{0 - (- 16)}$

Step 1.4

Simplify.

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Step 1.4.1

Reduce the expression by cancelling the common factors.

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Step 1.4.1.1

Cancel the common factor of $- 4 - (0)$ and $0 - (- 16)$ .

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Step 1.4.1.1.1

Rewrite $- 4$ as $- 1 (4)$ .

$m = \frac{- 1 \cdot 4 - (0)}{0 - (- 16)}$

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (4) - (0)$ .

$m = \frac{- 1 (4 + 0)}{0 - (- 16)}$

Step 1.4.1.1.3

Reorder terms.

$m = \frac{- 1 (4 + 0)}{0 - 16 \cdot - 1}$

Step 1.4.1.1.4

Factor $4$ out of $- 1 (4 + 0)$ .

$m = \frac{4 (- 1 (1 + 0))}{0 - 16 \cdot - 1}$

Step 1.4.1.1.5

Cancel the common factors.

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Step 1.4.1.1.5.1

Factor $4$ out of $0$ .

$m = \frac{4 (- 1 (1 + 0))}{4 (0) - 16 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $4$ out of $- 16 \cdot - 1$ .

$m = \frac{4 (- 1 (1 + 0))}{4 (0) + 4 (- 4 \cdot - 1)}$

Step 1.4.1.1.5.3

Factor $4$ out of $4 (0) + 4 (- 4 \cdot - 1)$ .

$m = \frac{4 (- 1 (1 + 0))}{4 (0 - 4 \cdot - 1)}$

Step 1.4.1.1.5.4

Cancel the common factor.

$m = \frac{4 (- 1 (1 + 0))}{4 (0 - 4 \cdot - 1)}$

Step 1.4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (1 + 0)}{0 - 4 \cdot - 1}$

Step 1.4.1.2

Add $1$ and $0$ .

$m = \frac{- 1 \cdot 1}{0 - 4 \cdot - 1}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 4$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{0 + 4}$

Step 1.4.2.2

Add $0$ and $4$ .

$m = \frac{- 1 \cdot 1}{4}$

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Multiply $- 1$ by $1$ .

$m = \frac{- 1}{4}$

Step 1.4.3.2

Move the negative in front of the fraction.

$m = - \frac{1}{4}$

Step 2

Use the slope $- \frac{1}{4}$ and a given point $(- 16, 0)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{4} \cdot (x - (- 16))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 0 = - \frac{1}{4} \cdot (x + 16)$

Step 4

Solve for $y$ .

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Step 4.1

Add $y$ and $0$ .

$y = - \frac{1}{4} \cdot (x + 16)$

Step 4.2

Simplify $- \frac{1}{4} \cdot (x + 16)$ .

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Step 4.2.1

Apply the distributive property.

$y = - \frac{1}{4} x - \frac{1}{4} \cdot 16$

Step 4.2.2

Combine $x$ and $\frac{1}{4}$ .

$y = - \frac{x}{4} - \frac{1}{4} \cdot 16$

Step 4.2.3

Cancel the common factor of $4$ .

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Step 4.2.3.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$y = - \frac{x}{4} + \frac{- 1}{4} \cdot 16$

Step 4.2.3.2

Factor $4$ out of $16$ .

$y = - \frac{x}{4} + \frac{- 1}{4} \cdot (4 (4))$

Step 4.2.3.3

Cancel the common factor.

$y = - \frac{x}{4} + \frac{- 1}{4} \cdot (4 \cdot 4)$

Step 4.2.3.4

Rewrite the expression.

$y = - \frac{x}{4} - 1 \cdot 4$

Step 4.2.4

Multiply $- 1$ by $4$ .

$y = - \frac{x}{4} - 4$

Step 5

Reorder terms.

$y = - (\frac{1}{4} x) - 4$

Step 6

Remove parentheses.

$y = - \frac{1}{4} x - 4$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{1}{4} x - 4$

Point-slope form:

$y + 0 = - \frac{1}{4} \cdot (x + 16)$

Step 8