Finite Math Examples

$(15, 0)$ , $(0, 3)$

Step 1

Find the slope of the line between $(15, 0)$ and $(0, 3)$ 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.

$m = \frac{3 - (0)}{0 - (15)}$

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 $0$ .

$m = \frac{3 + 0}{0 - (15)}$

Step 1.4.1.2

Add $3$ and $0$ .

$m = \frac{3}{0 - (15)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $15$ .

$m = \frac{3}{0 - 15}$

Step 1.4.2.2

Subtract $15$ from $0$ .

$m = \frac{3}{- 15}$

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 $3$ and $- 15$ .

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Step 1.4.3.1.1

Factor $3$ out of $3$ .

$m = \frac{3 (1)}{- 15}$

Step 1.4.3.1.2

Cancel the common factors.

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Step 1.4.3.1.2.1

Factor $3$ out of $- 15$ .

$m = \frac{3 \cdot 1}{3 \cdot - 5}$

Step 1.4.3.1.2.2

Cancel the common factor.

$m = \frac{3 \cdot 1}{3 \cdot - 5}$

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

Use the slope $- \frac{1}{5}$ and a given point $(15, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{5} \cdot (x - (15))$

Step 3

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

$y + 0 = - \frac{1}{5} \cdot (x - 15)$

Step 4

Solve for $y$ .

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Step 4.1

Add $y$ and $0$ .

$y = - \frac{1}{5} \cdot (x - 15)$

Step 4.2

Simplify $- \frac{1}{5} \cdot (x - 15)$ .

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Step 4.2.1

Apply the distributive property.

$y = - \frac{1}{5} x - \frac{1}{5} \cdot - 15$

Step 4.2.2

Combine $x$ and $\frac{1}{5}$ .

$y = - \frac{x}{5} - \frac{1}{5} \cdot - 15$

Step 4.2.3

Cancel the common factor of $5$ .

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Step 4.2.3.1

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

$y = - \frac{x}{5} + \frac{- 1}{5} \cdot - 15$

Step 4.2.3.2

Factor $5$ out of $- 15$ .

$y = - \frac{x}{5} + \frac{- 1}{5} \cdot (5 (- 3))$

Step 4.2.3.3

Cancel the common factor.

$y = - \frac{x}{5} + \frac{- 1}{5} \cdot (5 \cdot - 3)$

Step 4.2.3.4

Rewrite the expression.

$y = - \frac{x}{5} - 1 \cdot - 3$

Step 4.2.4

Multiply $- 1$ by $- 3$ .

$y = - \frac{x}{5} + 3$

Step 5

Reorder terms.

$y = - (\frac{1}{5} x) + 3$

Step 6

Remove parentheses.

$y = - \frac{1}{5} x + 3$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{1}{5} x + 3$

Point-slope form:

$y + 0 = - \frac{1}{5} \cdot (x - 15)$

Step 8