Precalculus Examples

$(0, 2)$ , $(4, - 3)$

Step 1

Find the slope of the line between $(0, 2)$ and $(4, - 3)$ 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.

$m = \frac{- 3 - (2)}{4 - (0)}$

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 $2$ .

$m = \frac{- 3 - 2}{4 - (0)}$

Step 1.4.1.2

Subtract $2$ from $- 3$ .

$m = \frac{- 5}{4 - (0)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $0$ .

$m = \frac{- 5}{4 + 0}$

Step 1.4.2.2

Add $4$ and $0$ .

$m = \frac{- 5}{4}$

Step 1.4.3

Move the negative in front of the fraction.

$m = - \frac{5}{4}$

Step 2

Use the slope $- \frac{5}{4}$ and a given point $(0, 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (2) = - \frac{5}{4} \cdot (x - (0))$

Step 3

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

$y - 2 = - \frac{5}{4} \cdot (x + 0)$

Step 4

Solve for $y$ .

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Step 4.1

Simplify $- \frac{5}{4} \cdot (x + 0)$ .

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Step 4.1.1

Add $x$ and $0$ .

$y - 2 = - \frac{5}{4} \cdot x$

Step 4.1.2

Combine $x$ and $\frac{5}{4}$ .

$y - 2 = - \frac{x \cdot 5}{4}$

Step 4.1.3

Move $5$ to the left of $x$ .

$y - 2 = - \frac{5 x}{4}$

Step 4.2

Add $2$ to both sides of the equation.

$y = - \frac{5 x}{4} + 2$

Step 5

Reorder terms.

$y = - (\frac{5}{4} x) + 2$

Step 6

Remove parentheses.

$y = - \frac{5}{4} x + 2$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{5}{4} x + 2$

Point-slope form:

$y - 2 = - \frac{5}{4} \cdot (x + 0)$

Step 8