Finite Math Examples

$(0, 14.1)$ , $(8, 17.2)$

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.

$m = \frac{17.2 - (14.1)}{8 - (0)}$

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 $14.1$ .

$m = \frac{17.2 - 14.1}{8 - (0)}$

Step 5.1.2

Subtract $14.1$ from $17.2$ .

$m = \frac{3.1}{8 - (0)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $0$ .

$m = \frac{3.1}{8 + 0}$

Step 5.2.2

Add $8$ and $0$ .

$m = \frac{3.1}{8}$

Step 5.3

Divide $3.1$ by $8$ .

$m = 0.3875$

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.

$y = (0.3875) \cdot x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (0.3875) \cdot (0) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$14.1 = (0.3875) \cdot (0) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $(0.3875) \cdot (0) + b = 14.1$ .

$(0.3875) \cdot (0) + b = 14.1$

Step 6.5.2

Simplify $(0.3875) \cdot (0) + b$ .

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Step 6.5.2.1

Multiply $0.3875$ by $0$ .

$0 + b = 14.1$

Step 6.5.2.2

Add $0$ and $b$ .

$b = 14.1$

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.

$y = 0.3875 x + 14.1$

Step 8