Trigonometry Examples

$g (x) = - 5 + \frac{10}{3} x$

Step 1

Rewrite the function as an equation.

$y = - 5 + \frac{10 x}{3}$

Step 2

Reorder $- 5$ and $\frac{10 x}{3}$ .

$y = \frac{10 x}{3} - 5$

Step 3

Rewrite in slope-intercept form.

Tap for more steps...

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

Reorder terms.

$y = \frac{10}{3} x - 5$

Step 4

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

Tap for more steps...

Step 4.1

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

$m = \frac{10}{3}$

$b = - 5$

Step 4.2

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

Slope: $\frac{10}{3}$

y-intercept: $(0, - 5)$

Slope: $\frac{10}{3}$

y-intercept: $(0, - 5)$

Step 5

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

Tap for more steps...

Step 5.1

Write in $y = m x + b$ form.

Tap for more steps...

Step 5.1.1

Reorder $- 5$ and $\frac{10 x}{3}$ .

$y = \frac{10 x}{3} - 5$

Step 5.1.2

Reorder terms.

$y = \frac{10}{3} x - 5$

Step 5.2

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

$\begin{array}{c} x & y \\ 0 & - 5 \\ 3 & 5 \end{array}$

Step 6

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

Slope: $\frac{10}{3}$

y-intercept: $(0, - 5)$

$\begin{array}{c} x & y \\ 0 & - 5 \\ 3 & 5 \end{array}$

Step 7