Finite Math Examples

f (10) = 0

$f (10) = 0$ ,

f (20) = 10

$f (20) = 10$

Step 1

f (10) = 0

$f (10) = 0$ , which means

(10, 0)

$(10, 0)$ is a point on the line.

f (20) = 10

$f (20) = 10$ , which means

(20, 10)

$(20, 10)$ is a point on the line, too.

(10, 0), (20, 10)

$(10, 0), (20, 10)$

Step 2

Find the slope of the line between

(10, 0)

$(10, 0)$ and

(20, 10)

$(20, 10)$ using

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of

y

$y$ over the change of

x

$x$ .

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Step 2.1

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 2.2

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 2.3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

m = \frac{10 - (0)}{20 - (10)}

$m = \frac{10 - (0)}{20 - (10)}$

Step 2.4

Simplify.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Multiply

- 1

$- 1$ by

0

$0$ .

m = \frac{10 + 0}{20 - (10)}

$m = \frac{10 + 0}{20 - (10)}$

Step 2.4.1.2

Add

10

$10$ and

0

$0$ .

m = \frac{10}{20 - (10)}

$m = \frac{10}{20 - (10)}$

m = \frac{10}{20 - (10)}

$m = \frac{10}{20 - (10)}$

Step 2.4.2

Simplify the denominator.

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Step 2.4.2.1

Multiply

- 1

$- 1$ by

10

$10$ .

m = \frac{10}{20 - 10}

$m = \frac{10}{20 - 10}$

Step 2.4.2.2

Subtract

10

$10$ from

20

$20$ .

m = \frac{10}{10}

$m = \frac{10}{10}$

m = \frac{10}{10}

$m = \frac{10}{10}$

Step 2.4.3

Divide

10

$10$ by

10

$10$ .

m = 1

$m = 1$

m = 1

$m = 1$

m = 1

$m = 1$

Step 3

Use the slope

1

$1$ and a given point

(10, 0)

$(10, 0)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

y - (0) = 1 \cdot (x - (10))

$y - (0) = 1 \cdot (x - (10))$

Step 4

Simplify the equation and keep it in point-slope form.

y + 0 = 1 \cdot (x - 10)

$y + 0 = 1 \cdot (x - 10)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Add

y

$y$ and

0

$0$ .

y = 1 \cdot (x - 10)

$y = 1 \cdot (x - 10)$

Step 5.2

Multiply

x - 10

$x - 10$ by

1

$1$ .

y = x - 10

$y = x - 10$

y = x - 10

$y = x - 10$

Step 6

Replace

y

$y$ by

f (x)

$f (x)$ .

f (x) = x - 10

$f (x) = x - 10$

Step 7