Finite Math Examples

$(4, 5)$ , $(8, 10)$

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.

$m = \frac{10 - (5)}{8 - (4)}$

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 $5$ .

$m = \frac{10 - 5}{8 - (4)}$

Step 5.1.2

Subtract $5$ from $10$ .

$m = \frac{5}{8 - (4)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $4$ .

$m = \frac{5}{8 - 4}$

Step 5.2.2

Subtract $4$ from $8$ .

$m = \frac{5}{4}$

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.

$y = (\frac{5}{4}) x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (\frac{5}{4}) \cdot (4) + b$

Step 6.4

Substitute the value of $y$ into the equation.

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

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $\frac{5}{4} \cdot 4 + b = 5$ .

$\frac{5}{4} \cdot 4 + b = 5$

Step 6.5.2

Cancel the common factor of $4$ .

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Step 6.5.2.1

Cancel the common factor.

$\frac{5}{4} \cdot 4 + b = 5$

Step 6.5.2.2

Rewrite the expression.

$5 + b = 5$

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 $5$ from both sides of the equation.

$b = 5 - 5$

Step 6.5.3.2

Subtract $5$ from $5$ .

$b = 0$

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.

$y = \frac{5}{4} x$

Step 8