Finite Math Examples

(5, 4)

$(5, 4)$ ,

(- 9, 7)

$(- 9, 7)$

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{7 - (4)}{- 9 - (5)}

$m = \frac{7 - (4)}{- 9 - (5)}$

Step 5

Finding the slope

m

$m$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply

- 1

$- 1$ by

4

$4$ .

m = \frac{7 - 4}{- 9 - (5)}

$m = \frac{7 - 4}{- 9 - (5)}$

Step 5.1.2

Subtract

4

$4$ from

7

$7$ .

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

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

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

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

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply

- 1

$- 1$ by

5

$5$ .

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

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

Step 5.2.2

Subtract

5

$5$ from

- 9

$- 9$ .

m = \frac{3}{- 14}

$m = \frac{3}{- 14}$

m = \frac{3}{- 14}

$m = \frac{3}{- 14}$

Step 5.3

Move the negative in front of the fraction.

m = - \frac{3}{14}

$m = - \frac{3}{14}$

m = - \frac{3}{14}

$m = - \frac{3}{14}$

Step 6

Find the value of

b

$b$ 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

$b$ .

y = m x + b

$y = m x + b$

Step 6.2

Substitute the value of

m

$m$ into the equation.

y = (- \frac{3}{14}) \cdot x + b

$y = (- \frac{3}{14}) \cdot x + b$

Step 6.3

Substitute the value of

x

$x$ into the equation.

y = (- \frac{3}{14}) \cdot (5) + b

$y = (- \frac{3}{14}) \cdot (5) + b$

Step 6.4

Substitute the value of

y

$y$ into the equation.

4 = (- \frac{3}{14}) \cdot (5) + b

$4 = (- \frac{3}{14}) \cdot (5) + b$

Step 6.5

Find the value of

b

$b$ .

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Step 6.5.1

Rewrite the equation as

- \frac{3}{14} \cdot 5 + b = 4

$- \frac{3}{14} \cdot 5 + b = 4$ .

- \frac{3}{14} \cdot 5 + b = 4

$- \frac{3}{14} \cdot 5 + b = 4$

Step 6.5.2

Simplify each term.

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Step 6.5.2.1

Multiply

- \frac{3}{14} \cdot 5

$- \frac{3}{14} \cdot 5$ .

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Step 6.5.2.1.1

Multiply

5

$5$ by

- 1

$- 1$ .

- 5 (\frac{3}{14}) + b = 4

$- 5 (\frac{3}{14}) + b = 4$

Step 6.5.2.1.2

Combine

- 5

$- 5$ and

\frac{3}{14}

$\frac{3}{14}$ .

\frac{- 5 \cdot 3}{14} + b = 4

$\frac{- 5 \cdot 3}{14} + b = 4$

Step 6.5.2.1.3

Multiply

- 5

$- 5$ by

3

$3$ .

\frac{- 15}{14} + b = 4

$\frac{- 15}{14} + b = 4$

Step 6.5.2.2

Move the negative in front of the fraction.

$- \frac{15}{14} + b = 4$

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

Add

$\frac{15}{14}$ to both sides of the equation.

$b = 4 + \frac{15}{14}$

Step 6.5.3.2

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{14}{14}$ .

$b = 4 \cdot \frac{14}{14} + \frac{15}{14}$

Step 6.5.3.3

Combine

$4$ and

$\frac{14}{14}$ .

$b = \frac{4 \cdot 14}{14} + \frac{15}{14}$

Step 6.5.3.4

Combine the numerators over the common denominator.

$b = \frac{4 \cdot 14 + 15}{14}$

Step 6.5.3.5

Simplify the numerator.

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Step 6.5.3.5.1

Multiply

$4$ by

$14$ .

$b = \frac{56 + 15}{14}$

Step 6.5.3.5.2

Add

$56$ and

$15$ .

$b = \frac{71}{14}$

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.

$y = - \frac{3}{14} x + \frac{71}{14}$

Step 8

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