Precalculus Examples

$f (x) = 6 (x - 8) + 5$

Step 1

Write $f (x) = 6 (x - 8) + 5$ as an equation.

$y = 6 (x - 8) + 5$

Step 2

Simplify $6 (x - 8) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$y = 6 x + 6 \cdot - 8 + 5$

Step 2.1.2

Multiply $6$ by $- 8$ .

$y = 6 x - 48 + 5$

Step 2.2

Add $- 48$ and $5$ .

$y = 6 x - 43$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = 6 (0) - 43$

Step 4.2

Simplify $6 (0) - 43$ .

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Step 4.2.1

Multiply $6$ by $0$ .

$y = 0 - 43$

Step 4.2.2

Subtract $43$ from $0$ .

$y = - 43$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, - 43)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = 6 (1) - 43$

Step 5.2

Simplify $6 (1) - 43$ .

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Step 5.2.1

Multiply $6$ by $1$ .

$y = 6 - 43$

Step 5.2.2

Subtract $43$ from $6$ .

$y = - 37$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, - 37)$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

$y = 6 (2) - 43$

Step 6.2

Simplify $6 (2) - 43$ .

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Step 6.2.1

Multiply $6$ by $2$ .

$y = 12 - 43$

Step 6.2.2

Subtract $43$ from $12$ .

$y = - 31$

Step 6.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - 31)$

Step 7

These are three possible solutions to the equation.

$(0, - 43), (1, - 37), (2, - 31)$

Step 8

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