Finite Math Examples

(- 48, 0)

$(- 48, 0)$ ,

(0, - 8)

$(0, - 8)$

Step 1

Use

y = m x + b

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

m

$m$ represents the slope and

b

$b$ represents the y-intercept.

To calculate the equation of the line, use the

y = m x + b

$y = m x + b$ format.

Step 2

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

m = \frac{(change in y)}{(change in x)}

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

Step 3

The change in

x

$x$ is equal to the difference in x-coordinates (also called run), and the change in

y

$y$ is equal to the difference in y-coordinates (also called rise).

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

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

Step 4

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

m = \frac{- 8 - (0)}{0 - (- 48)}

$m = \frac{- 8 - (0)}{0 - (- 48)}$

Step 5

Finding the slope

m

$m$ .

Tap for more steps...

Step 5.1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 5.1.1

Cancel the common factor of

- 8 - (0)

$- 8 - (0)$ and

0 - (- 48)

$0 - (- 48)$ .

Tap for more steps...

Step 5.1.1.1

Rewrite

- 8

$- 8$ as

- 1 (8)

$- 1 (8)$ .

m = \frac{- 1 \cdot 8 - (0)}{0 - (- 48)}

$m = \frac{- 1 \cdot 8 - (0)}{0 - (- 48)}$

Step 5.1.1.2

Factor

- 1

$- 1$ out of

- 1 (8) - (0)

$- 1 (8) - (0)$ .

m = \frac{- 1 (8 + 0)}{0 - (- 48)}

$m = \frac{- 1 (8 + 0)}{0 - (- 48)}$

Step 5.1.1.3

Reorder terms.

m = \frac{- 1 (8 + 0)}{0 - 48 \cdot - 1}

$m = \frac{- 1 (8 + 0)}{0 - 48 \cdot - 1}$

Step 5.1.1.4

Factor

8

$8$ out of

- 1 (8 + 0)

$- 1 (8 + 0)$ .

m = \frac{8 (- 1 (1 + 0))}{0 - 48 \cdot - 1}

$m = \frac{8 (- 1 (1 + 0))}{0 - 48 \cdot - 1}$

Step 5.1.1.5

Cancel the common factors.

Tap for more steps...

Step 5.1.1.5.1

Factor

8

$8$ out of

0

$0$ .

m = \frac{8 (- 1 (1 + 0))}{8 (0) - 48 \cdot - 1}

$m = \frac{8 (- 1 (1 + 0))}{8 (0) - 48 \cdot - 1}$

Step 5.1.1.5.2

Factor

8

$8$ out of

- 48 \cdot - 1

$- 48 \cdot - 1$ .

m = \frac{8 (- 1 (1 + 0))}{8 (0) + 8 (- 6 \cdot - 1)}

$m = \frac{8 (- 1 (1 + 0))}{8 (0) + 8 (- 6 \cdot - 1)}$

Step 5.1.1.5.3

Factor

8

$8$ out of

8 (0) + 8 (- 6 \cdot - 1)

$8 (0) + 8 (- 6 \cdot - 1)$ .

m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}

$m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}$

Step 5.1.1.5.4

Cancel the common factor.

m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}

$m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}$

Step 5.1.1.5.5

Rewrite the expression.

m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}

$m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}$

m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}

$m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}$

m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}

$m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}$

Step 5.1.2

Add

1

$1$ and

0

$0$ .

m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}

$m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}$

m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}

$m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}$

Step 5.2

Simplify the denominator.

Tap for more steps...

Step 5.2.1

Multiply

- 6

$- 6$ by

- 1

$- 1$ .

m = \frac{- 1 \cdot 1}{0 + 6}

$m = \frac{- 1 \cdot 1}{0 + 6}$

Step 5.2.2

Add

0

$0$ and

6

$6$ .

m = \frac{- 1 \cdot 1}{6}

$m = \frac{- 1 \cdot 1}{6}$

m = \frac{- 1 \cdot 1}{6}

$m = \frac{- 1 \cdot 1}{6}$

Step 5.3

Simplify the expression.

Tap for more steps...

Step 5.3.1

Multiply

- 1

$- 1$ by

1

$1$ .

m = \frac{- 1}{6}

$m = \frac{- 1}{6}$

Step 5.3.2

Move the negative in front of the fraction.

m = - \frac{1}{6}

$m = - \frac{1}{6}$

m = - \frac{1}{6}

$m = - \frac{1}{6}$

m = - \frac{1}{6}

$m = - \frac{1}{6}$

Step 6

Find the value of

b

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

Tap for more steps...

Step 6.1

Use the formula for the equation of a line to find

b

$b$ .

y = m x + b

$y = m x + b$

Step 6.2

Substitute the value of

m

$m$ into the equation.

y = (- \frac{1}{6}) \cdot x + b

$y = (- \frac{1}{6}) \cdot x + b$

Step 6.3

Substitute the value of

x

$x$ into the equation.

y = (- \frac{1}{6}) \cdot (- 48) + b

$y = (- \frac{1}{6}) \cdot (- 48) + b$

Step 6.4

Substitute the value of

y

$y$ into the equation.

0 = (- \frac{1}{6}) \cdot (- 48) + b

$0 = (- \frac{1}{6}) \cdot (- 48) + b$

Step 6.5

Find the value of

b

$b$ .

Tap for more steps...

Step 6.5.1

Rewrite the equation as

- \frac{1}{6} \cdot - 48 + b = 0

$- \frac{1}{6} \cdot - 48 + b = 0$ .

- \frac{1}{6} \cdot - 48 + b = 0

$- \frac{1}{6} \cdot - 48 + b = 0$

Step 6.5.2

Simplify each term.

Tap for more steps...

Step 6.5.2.1

Cancel the common factor of

6

$6$ .

Tap for more steps...

Step 6.5.2.1.1

Move the leading negative in

- \frac{1}{6}

$- \frac{1}{6}$ into the numerator.

\frac{- 1}{6} \cdot - 48 + b = 0

$\frac{- 1}{6} \cdot - 48 + b = 0$

Step 6.5.2.1.2

Factor

6

$6$ out of

- 48

$- 48$ .

\frac{- 1}{6} \cdot (6 (- 8)) + b = 0

$\frac{- 1}{6} \cdot (6 (- 8)) + b = 0$

Step 6.5.2.1.3

Cancel the common factor.

\frac{- 1}{6} \cdot (6 \cdot - 8) + b = 0

$\frac{- 1}{6} \cdot (6 \cdot - 8) + b = 0$

Step 6.5.2.1.4

Rewrite the expression.

- 1 \cdot - 8 + b = 0

$- 1 \cdot - 8 + b = 0$

- 1 \cdot - 8 + b = 0

$- 1 \cdot - 8 + b = 0$

Step 6.5.2.2

Multiply

- 1

$- 1$ by

- 8

$- 8$ .

8 + b = 0

$8 + b = 0$

8 + b = 0

$8 + b = 0$

Step 6.5.3

Subtract

8

$8$ from both sides of the equation.

b = - 8

$b = - 8$

b = - 8

$b = - 8$

b = - 8

$b = - 8$

Step 7

Now that the values of

m

$m$ (slope) and

b

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

y = m x + b

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

y = - \frac{1}{6} x - 8

$y = - \frac{1}{6} x - 8$

Step 8