Trigonometry Examples

$f (x) = 4 (1.1) - x$

Step 1

Rewrite the function as an equation.

$y = 4.4 - x$

Step 2

Reorder $4.4$ and $- x$ .

$y = - x + 4.4$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

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Step 3.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 3.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 1$

$b = 4.4$

Step 3.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 1$

y-intercept: $(0, 4.4)$

Slope: $- 1$

y-intercept: $(0, 4.4)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 4.1

Reorder $4.4$ and $- x$ .

$y = - x + 4.4$

Step 4.2

Find the x-intercept.

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Step 4.2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - x + 4.4$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $- x + 4.4 = 0$ .

$- x + 4.4 = 0$

Step 4.2.2.2

Subtract $4.4$ from both sides of the equation.

$- x = - 4.4$

Step 4.2.2.3

Divide each term in $- x = - 4.4$ by $- 1$ and simplify.

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Step 4.2.2.3.1

Divide each term in $- x = - 4.4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4.4}{- 1}$

Step 4.2.2.3.2

Simplify the left side.

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Step 4.2.2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4.4}{- 1}$

Step 4.2.2.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 4.4}{- 1}$

Step 4.2.2.3.3

Simplify the right side.

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Step 4.2.2.3.3.1

Divide $- 4.4$ by $- 1$ .

$x = 4.4$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(4.4, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - (0) + 4.4$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

$y = - (0) + 4.4$

Step 4.3.2.2

Simplify $- (0) + 4.4$ .

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Step 4.3.2.2.1

Multiply $- 1$ by $0$ .

$y = 0 + 4.4$

Step 4.3.2.2.2

Add $0$ and $4.4$ .

$y = 4.4$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, 4.4)$

Step 4.4

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 4.4 \\ 4.4 & 0 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- 1$

y-intercept: $(0, 4.4)$

$\begin{array}{c} x & y \\ 0 & 4.4 \\ 4.4 & 0 \end{array}$

Step 6