Pre-Algebra Examples

$(- 5, 9)$ ,

$(3, 0)$

Step 1

Use

$y = m x + b$ to calculate the equation of the line, where

$m$ represents the slope and

$b$ represents the y-intercept.

To calculate the equation of the line, use the

$y = m x + b$ format.

Step 2

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 3

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 4

Substitute in the values of

$x$ and

$y$ into the equation to find the slope.

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

Step 5

Finding the slope

$m$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply

$- 1$ by

$9$ .

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

Step 5.1.2

Subtract

$9$ from

$0$ .

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

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply

$- 1$ by

$- 5$ .

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

Step 5.2.2

Add

$3$ and

$5$ .

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

Step 5.3

Move the negative in front of the fraction.

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

Step 6

Find the value of

$b$ using the formula for the equation of a line.

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Step 6.1

Use the formula for the equation of a line to find

$b$ .

$y = m x + b$

Step 6.2

Substitute the value of

$m$ into the equation.

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

Step 6.3

Substitute the value of

$x$ into the equation.

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

Step 6.4

Substitute the value of

$y$ into the equation.

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

Step 6.5

Find the value of

$b$ .

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Step 6.5.1

Rewrite the equation as

$- \frac{9}{8} \cdot - 5 + b = 9$ .

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

Step 6.5.2

Multiply

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

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Step 6.5.2.1

Multiply

$- 5$ by

$- 1$ .

$5 (\frac{9}{8}) + b = 9$

Step 6.5.2.2

Combine

$5$ and

$\frac{9}{8}$ .

$\frac{5 \cdot 9}{8} + b = 9$

Step 6.5.2.3

Multiply

$5$ by

$9$ .

$\frac{45}{8} + b = 9$

Step 6.5.3

Move all terms not containing

$b$ to the right side of the equation.

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Step 6.5.3.1

Subtract

$\frac{45}{8}$ from both sides of the equation.

$b = 9 - \frac{45}{8}$

Step 6.5.3.2

To write

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

$\frac{8}{8}$ .

$b = 9 \cdot \frac{8}{8} - \frac{45}{8}$

Step 6.5.3.3

Combine

$9$ and

$\frac{8}{8}$ .

$b = \frac{9 \cdot 8}{8} - \frac{45}{8}$

Step 6.5.3.4

Combine the numerators over the common denominator.

$b = \frac{9 \cdot 8 - 45}{8}$

Step 6.5.3.5

Simplify the numerator.

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Step 6.5.3.5.1

Multiply

$9$ by

$8$ .

$b = \frac{72 - 45}{8}$

Step 6.5.3.5.2

Subtract

$45$ from

$72$ .

$b = \frac{27}{8}$

Step 7

Now that the values of

$m$ (slope) and

$b$ (y-intercept) are known, substitute them into

$y = m x + b$ to find the equation of the line.

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

Step 8

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