Finite Math Examples

$(- 1, 7)$ , $(- 8, - 8)$

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.

$m = \frac{- 8 - (7)}{- 8 - (- 1)}$

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 $7$ .

$m = \frac{- 8 - 7}{- 8 - (- 1)}$

Step 5.1.2

Subtract $7$ from $- 8$ .

$m = \frac{- 15}{- 8 - (- 1)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 15}{- 8 + 1}$

Step 5.2.2

Add $- 8$ and $1$ .

$m = \frac{- 15}{- 7}$

Step 5.3

Dividing two negative values results in a positive value.

$m = \frac{15}{7}$

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.

$y = (\frac{15}{7}) x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (\frac{15}{7}) \cdot (- 1) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$7 = (\frac{15}{7}) \cdot (- 1) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $\frac{15}{7} \cdot - 1 + b = 7$ .

$\frac{15}{7} \cdot - 1 + b = 7$

Step 6.5.2

Simplify each term.

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Step 6.5.2.1

Multiply $\frac{15}{7} \cdot - 1$ .

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Step 6.5.2.1.1

Combine $\frac{15}{7}$ and $- 1$ .

$\frac{15 \cdot - 1}{7} + b = 7$

Step 6.5.2.1.2

Multiply $15$ by $- 1$ .

$\frac{- 15}{7} + b = 7$

Step 6.5.2.2

Move the negative in front of the fraction.

$- \frac{15}{7} + b = 7$

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 $\frac{15}{7}$ to both sides of the equation.

$b = 7 + \frac{15}{7}$

Step 6.5.3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$b = 7 \cdot \frac{7}{7} + \frac{15}{7}$

Step 6.5.3.3

Combine $7$ and $\frac{7}{7}$ .

$b = \frac{7 \cdot 7}{7} + \frac{15}{7}$

Step 6.5.3.4

Combine the numerators over the common denominator.

$b = \frac{7 \cdot 7 + 15}{7}$

Step 6.5.3.5

Simplify the numerator.

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Step 6.5.3.5.1

Multiply $7$ by $7$ .

$b = \frac{49 + 15}{7}$

Step 6.5.3.5.2

Add $49$ and $15$ .

$b = \frac{64}{7}$

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.

$y = \frac{15}{7} x + \frac{64}{7}$

Step 8