Precalculus Examples

(- 5, 9)

$(- 5, 9)$ ,

$(3, 0)$

Step 1

Find the slope of the line between

$(- 5, 9)$ and

$(3, 0)$ using

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of

$y$ over the change of

$x$ .

Tap for more steps...

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.

$m = \frac{0 - (9)}{3 - (- 5)}$

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

Simplify the numerator.

Tap for more steps...

Step 1.4.1.1

Multiply

$- 1$ by

$9$ .

$m = \frac{0 - 9}{3 - (- 5)}$

Step 1.4.1.2

Subtract

$9$ from

$0$ .

$m = \frac{- 9}{3 - (- 5)}$

Step 1.4.2

Simplify the denominator.

Tap for more steps...

Step 1.4.2.1

Multiply

$- 1$ by

$- 5$ .

$m = \frac{- 9}{3 + 5}$

Step 1.4.2.2

Add

$3$ and

$5$ .

$m = \frac{- 9}{8}$

Step 1.4.3

Move the negative in front of the fraction.

$m = - \frac{9}{8}$

Step 2

Use the slope

$- \frac{9}{8}$ and a given point

$(- 5, 9)$ 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

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

$y - (9) = - \frac{9}{8} \cdot (x - (- 5))$

Step 3

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

$y - 9 = - \frac{9}{8} \cdot (x + 5)$

Step 4

Solve for

$y$ .

Tap for more steps...

Step 4.1

Simplify

$- \frac{9}{8} \cdot (x + 5)$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$y - 9 = 0 + 0 - \frac{9}{8} \cdot (x + 5)$

Step 4.1.2

Simplify by adding zeros.

$y - 9 = - \frac{9}{8} \cdot (x + 5)$

Step 4.1.3

Apply the distributive property.

$y - 9 = - \frac{9}{8} x - \frac{9}{8} \cdot 5$

Step 4.1.4

Combine

$x$ and

$\frac{9}{8}$ .

$y - 9 = - \frac{x \cdot 9}{8} - \frac{9}{8} \cdot 5$

Step 4.1.5

Multiply

$- \frac{9}{8} \cdot 5$ .

Tap for more steps...

Step 4.1.5.1

Multiply

$5$ by

$- 1$ .

$y - 9 = - \frac{x \cdot 9}{8} - 5 (\frac{9}{8})$

Step 4.1.5.2

Combine

$- 5$ and

$\frac{9}{8}$ .

$y - 9 = - \frac{x \cdot 9}{8} + \frac{- 5 \cdot 9}{8}$

Step 4.1.5.3

Multiply

$- 5$ by

$9$ .

$y - 9 = - \frac{x \cdot 9}{8} + \frac{- 45}{8}$

Step 4.1.6

Simplify each term.

Tap for more steps...

Step 4.1.6.1

Move

$9$ to the left of

$x$ .

$y - 9 = - \frac{9 \cdot x}{8} + \frac{- 45}{8}$

Step 4.1.6.2

Move the negative in front of the fraction.

$y - 9 = - \frac{9 x}{8} - \frac{45}{8}$

Step 4.2

Move all terms not containing

$y$ to the right side of the equation.

Tap for more steps...

Step 4.2.1

Add

$9$ to both sides of the equation.

$y = - \frac{9 x}{8} - \frac{45}{8} + 9$

Step 4.2.2

To write

$9$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$y = - \frac{9 x}{8} - \frac{45}{8} + 9 \cdot \frac{8}{8}$

Step 4.2.3

Combine

$9$ and

$\frac{8}{8}$ .

$y = - \frac{9 x}{8} - \frac{45}{8} + \frac{9 \cdot 8}{8}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = - \frac{9 x}{8} + \frac{- 45 + 9 \cdot 8}{8}$

Step 4.2.5

Simplify the numerator.

Tap for more steps...

Step 4.2.5.1

Multiply

$9$ by

$8$ .

$y = - \frac{9 x}{8} + \frac{- 45 + 72}{8}$

Step 4.2.5.2

Add

$- 45$ and

$72$ .

$y = - \frac{9 x}{8} + \frac{27}{8}$

Step 5

Reorder terms.

$y = - (\frac{9}{8} x) + \frac{27}{8}$

Step 6

Remove parentheses.

$y = - \frac{9}{8} x + \frac{27}{8}$

Step 7

List the equation in different forms.

Slope-intercept form:

$y = - \frac{9}{8} x + \frac{27}{8}$

Point-slope form:

$y - 9 = - \frac{9}{8} \cdot (x + 5)$

Step 8

Enter YOUR Problem