Finite Math Examples

$(1, - 2)$ , $(3, 6)$

Find the slope of the line between $(1, - 2)$ and $(3, 6)$ 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.

$m = \frac{6 - (- 2)}{3 - (1)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $- 2$ .

$m = \frac{6 + 2}{3 - (1)}$

Add $6$ and $2$ .

$m = \frac{8}{3 - (1)}$

Simplify the denominator.

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Multiply $- 1$ by $1$ .

$m = \frac{8}{3 - 1}$

Subtract $1$ from $3$ .

$m = \frac{8}{2}$

Divide $8$ by $2$ .

$m = 4$

Use the slope $m = 4$ and one of the given points such as $(1, - 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$(y - (- 2)) = 4 \cdot (x - (1))$

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

$(y - (- 2)) = 4 \cdot (x - (1))$

Multiply $- 1$ by $- 2$ .

$y + 2 = 4 \cdot (x - (1))$

Simplify the right side.

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Simplify the expression.

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Multiply $- 1$ by $1$ .

$y + 2 = 4 \cdot (x - 1)$

Multiply $4$ by $x - 1$ .

$y + 2 = 4 (x - 1)$

Apply the distributive property.

$y + 2 = 4 x + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$y + 2 = 4 x - 4$

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

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Subtract $2$ from both sides of the equation.

$y = - 2 + 4 x - 4$

Subtract $4$ from $- 2$ .

$y = 4 x - 6$

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