Finite Math Examples

$(332, 0)$ , $(360, 40)$

Step 1

Find the slope of the line between $(332, 0)$ and $(360, 40)$ 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.

$m = \frac{40 - (0)}{360 - (332)}$

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 $0$ .

$m = \frac{40 + 0}{360 - (332)}$

Step 1.4.1.2

Add $40$ and $0$ .

$m = \frac{40}{360 - (332)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $332$ .

$m = \frac{40}{360 - 332}$

Step 1.4.2.2

Subtract $332$ from $360$ .

$m = \frac{40}{28}$

Step 1.4.3

Cancel the common factor of $40$ and $28$ .

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Step 1.4.3.1

Factor $4$ out of $40$ .

$m = \frac{4 (10)}{28}$

Step 1.4.3.2

Cancel the common factors.

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Step 1.4.3.2.1

Factor $4$ out of $28$ .

$m = \frac{4 \cdot 10}{4 \cdot 7}$

Step 1.4.3.2.2

Cancel the common factor.

$m = \frac{4 \cdot 10}{4 \cdot 7}$

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{10}{7}$

Step 2

Use the slope $\frac{10}{7}$ and a given point $(332, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{10}{7} \cdot (x - (332))$

Step 3

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

$y + 0 = \frac{10}{7} \cdot (x - 332)$

Step 4

Solve for $y$ .

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Step 4.1

Add $y$ and $0$ .

$y = \frac{10}{7} \cdot (x - 332)$

Step 4.2

Simplify $\frac{10}{7} \cdot (x - 332)$ .

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Step 4.2.1

Apply the distributive property.

$y = \frac{10}{7} x + \frac{10}{7} \cdot - 332$

Step 4.2.2

Combine $\frac{10}{7}$ and $x$ .

$y = \frac{10 x}{7} + \frac{10}{7} \cdot - 332$

Step 4.2.3

Multiply $\frac{10}{7} \cdot - 332$ .

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Step 4.2.3.1

Combine $\frac{10}{7}$ and $- 332$ .

$y = \frac{10 x}{7} + \frac{10 \cdot - 332}{7}$

Step 4.2.3.2

Multiply $10$ by $- 332$ .

$y = \frac{10 x}{7} + \frac{- 3320}{7}$

Step 4.2.4

Move the negative in front of the fraction.

$y = \frac{10 x}{7} - \frac{3320}{7}$

Step 5

Reorder terms.

$y = \frac{10}{7} x - \frac{3320}{7}$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{10}{7} x - \frac{3320}{7}$

Point-slope form:

$y + 0 = \frac{10}{7} \cdot (x - 332)$

Step 7