Finite Math Examples

$(2, - 3)$ , $(- 10, - 12)$

Step 1

Find the slope of the line between $(2, - 3)$ and $(- 10, - 12)$ 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.

$m = \frac{- 12 - (- 3)}{- 10 - (2)}$

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 $- 3$ .

$m = \frac{- 12 + 3}{- 10 - (2)}$

Step 1.4.1.2

Add $- 12$ and $3$ .

$m = \frac{- 9}{- 10 - (2)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $2$ .

$m = \frac{- 9}{- 10 - 2}$

Step 1.4.2.2

Subtract $2$ from $- 10$ .

$m = \frac{- 9}{- 12}$

Step 1.4.3

Cancel the common factor of $- 9$ and $- 12$ .

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Step 1.4.3.1

Factor $- 3$ out of $- 9$ .

$m = \frac{- 3 \cdot 3}{- 12}$

Step 1.4.3.2

Cancel the common factors.

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Step 1.4.3.2.1

Factor $- 3$ out of $- 12$ .

$m = \frac{- 3 \cdot 3}{- 3 \cdot 4}$

Step 1.4.3.2.2

Cancel the common factor.

$m = \frac{- 3 \cdot 3}{- 3 \cdot 4}$

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{3}{4}$

Step 2

Use the slope $\frac{3}{4}$ and a given point $(2, - 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 3) = \frac{3}{4} \cdot (x - (2))$

Step 3

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

$y + 3 = \frac{3}{4} \cdot (x - 2)$

Step 4

Solve for $y$ .

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Step 4.1

Simplify $\frac{3}{4} \cdot (x - 2)$ .

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Step 4.1.1

Rewrite.

$y + 3 = 0 + 0 + \frac{3}{4} \cdot (x - 2)$

Step 4.1.2

Simplify by adding zeros.

$y + 3 = \frac{3}{4} \cdot (x - 2)$

Step 4.1.3

Apply the distributive property.

$y + 3 = \frac{3}{4} x + \frac{3}{4} \cdot - 2$

Step 4.1.4

Combine $\frac{3}{4}$ and $x$ .

$y + 3 = \frac{3 x}{4} + \frac{3}{4} \cdot - 2$

Step 4.1.5

Cancel the common factor of $2$ .

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Step 4.1.5.1

Factor $2$ out of $4$ .

$y + 3 = \frac{3 x}{4} + \frac{3}{2 (2)} \cdot - 2$

Step 4.1.5.2

Factor $2$ out of $- 2$ .

$y + 3 = \frac{3 x}{4} + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 4.1.5.3

Cancel the common factor.

$y + 3 = \frac{3 x}{4} + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 4.1.5.4

Rewrite the expression.

$y + 3 = \frac{3 x}{4} + \frac{3}{2} \cdot - 1$

Step 4.1.6

Combine $\frac{3}{2}$ and $- 1$ .

$y + 3 = \frac{3 x}{4} + \frac{3 \cdot - 1}{2}$

Step 4.1.7

Simplify the expression.

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Step 4.1.7.1

Multiply $3$ by $- 1$ .

$y + 3 = \frac{3 x}{4} + \frac{- 3}{2}$

Step 4.1.7.2

Move the negative in front of the fraction.

$y + 3 = \frac{3 x}{4} - \frac{3}{2}$

Step 4.2

Move all terms not containing $y$ to the right side of the equation.

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$y = \frac{3 x}{4} - \frac{3}{2} - 3$

Step 4.2.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{3 x}{4} - \frac{3}{2} - 3 \cdot \frac{2}{2}$

Step 4.2.3

Combine $- 3$ and $\frac{2}{2}$ .

$y = \frac{3 x}{4} - \frac{3}{2} + \frac{- 3 \cdot 2}{2}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{3 x}{4} + \frac{- 3 - 3 \cdot 2}{2}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 3$ by $2$ .

$y = \frac{3 x}{4} + \frac{- 3 - 6}{2}$

Step 4.2.5.2

Subtract $6$ from $- 3$ .

$y = \frac{3 x}{4} + \frac{- 9}{2}$

Step 4.2.6

Move the negative in front of the fraction.

$y = \frac{3 x}{4} - \frac{9}{2}$

Step 5

Reorder terms.

$y = \frac{3}{4} x - \frac{9}{2}$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{3}{4} x - \frac{9}{2}$

Point-slope form:

$y + 3 = \frac{3}{4} \cdot (x - 2)$

Step 7