Finite Math Examples

$(0, 9)$ , $(8, 6)$

Find the slope of the line between $(0, 9)$ and $(8, 6)$ 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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Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

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).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{6 - (9)}{8 - (0)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $9$ .

$m = \frac{6 - 9}{8 - (0)}$

Subtract $9$ from $6$ .

$m = \frac{- 3}{8 - (0)}$

Simplify the denominator.

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Remove parentheses.

$m = \frac{- 3}{8 - (0)}$

Multiply $- 1$ by $0$ .

$m = \frac{- 3}{8 + 0}$

Add $8$ and $0$ .

$m = \frac{- 3}{8}$

Move the negative in front of the fraction.

$m = - \frac{3}{8}$

Use the slope $m = - \frac{3}{8}$ and one of the given points such as $(0, 9)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $(y - y_{1}) = m \cdot (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$(y - (9)) = - \frac{3}{8} \cdot (x - (0))$

Solve for $y$ to get the equation.

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After finding the slope between the points, use point-slope form to set up the equation. Point-slope is derived from the equation for slope $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$(y - (9)) = - \frac{3}{8} \cdot (x - (0))$

Multiply $- 1$ by $9$ .

$y - 9 = - \frac{3}{8} \cdot (x - (0))$

Simplify the right side.

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Subtract $0$ from $x$ .

$y - 9 = - \frac{3}{8} x$

Simplify $- \frac{3}{8} x$ .

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Write $x$ as a fraction with denominator $1$ .

$y - 9 = - (\frac{x}{1} \cdot \frac{3}{8})$

Multiply $\frac{x}{1}$ and $\frac{3}{8}$ .

$y - 9 = - \frac{x \cdot 3}{8}$

Move $3$ to the left of the expression $x \cdot 3$ .

$y - 9 = - \frac{3 \cdot x}{8}$

Multiply $3$ by $x$ .

$y - 9 = - \frac{3 x}{8}$

Add $9$ to both sides of the equation.

$y = 9 - \frac{3 x}{8}$

The final answer is the equation in slope-intercept form.

$y = - \frac{3}{8} x + 9$

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