Finite Math Examples

$(1940, 241681)$ , $(2005, 1186412)$

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.

$m = \frac{1186412 - (241681)}{2005 - (1940)}$

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 $241681$ .

$m = \frac{1186412 - 241681}{2005 - (1940)}$

Step 5.1.2

Subtract $241681$ from $1186412$ .

$m = \frac{944731}{2005 - (1940)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $1940$ .

$m = \frac{944731}{2005 - 1940}$

Step 5.2.2

Subtract $1940$ from $2005$ .

$m = \frac{944731}{65}$

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.

$y = (\frac{944731}{65}) x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (\frac{944731}{65}) \cdot (1940) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$241681 = (\frac{944731}{65}) \cdot (1940) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $\frac{944731}{65} \cdot 1940 + b = 241681$ .

$\frac{944731}{65} \cdot 1940 + b = 241681$

Step 6.5.2

Simplify each term.

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Step 6.5.2.1

Cancel the common factor of $5$ .

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Step 6.5.2.1.1

Factor $5$ out of $65$ .

$\frac{944731}{5 (13)} \cdot 1940 + b = 241681$

Step 6.5.2.1.2

Factor $5$ out of $1940$ .

$\frac{944731}{5 \cdot 13} \cdot (5 \cdot 388) + b = 241681$

Step 6.5.2.1.3

Cancel the common factor.

$\frac{944731}{5 \cdot 13} \cdot (5 \cdot 388) + b = 241681$

Step 6.5.2.1.4

Rewrite the expression.

$\frac{944731}{13} \cdot 388 + b = 241681$

Step 6.5.2.2

Combine $\frac{944731}{13}$ and $388$ .

$\frac{944731 \cdot 388}{13} + b = 241681$

Step 6.5.2.3

Multiply $944731$ by $388$ .

$\frac{366555628}{13} + b = 241681$

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 $\frac{366555628}{13}$ from both sides of the equation.

$b = 241681 - \frac{366555628}{13}$

Step 6.5.3.2

To write $241681$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$b = 241681 \cdot \frac{13}{13} - \frac{366555628}{13}$

Step 6.5.3.3

Combine $241681$ and $\frac{13}{13}$ .

$b = \frac{241681 \cdot 13}{13} - \frac{366555628}{13}$

Step 6.5.3.4

Combine the numerators over the common denominator.

$b = \frac{241681 \cdot 13 - 366555628}{13}$

Step 6.5.3.5

Simplify the numerator.

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Step 6.5.3.5.1

Multiply $241681$ by $13$ .

$b = \frac{3141853 - 366555628}{13}$

Step 6.5.3.5.2

Subtract $366555628$ from $3141853$ .

$b = \frac{- 363413775}{13}$

Step 6.5.3.6

Move the negative in front of the fraction.

$b = - \frac{363413775}{13}$

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.

$y = \frac{944731}{65} x - \frac{363413775}{13}$

Step 8