Trigonometry Examples

$y = \frac{- 8 x + 6000}{5}$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

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

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Step 1.2.1

Apply the distributive property.

$y = - \frac{8 x + 8 \cdot - 750}{5}$

Step 1.2.2

Multiply $8$ by $- 750$ .

$y = - \frac{8 x - 6000}{5}$

Step 1.2.3

Split the fraction $\frac{8 x - 6000}{5}$ into two fractions.

$y = - (\frac{8 x}{5} + \frac{- 6000}{5})$

Step 1.2.4

Divide $- 6000$ by $5$ .

$y = - (\frac{8 x}{5} - 1200)$

Step 1.2.5

To write $- 1200$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - (\frac{8 x}{5} - 1200 \cdot \frac{5}{5})$

Step 1.2.6

Combine $- 1200$ and $\frac{5}{5}$ .

$y = - (\frac{8 x}{5} + \frac{- 1200 \cdot 5}{5})$

Step 1.2.7

Combine the numerators over the common denominator.

$y = - \frac{8 x - 1200 \cdot 5}{5}$

Step 1.2.8

Simplify the numerator.

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Step 1.2.8.1

Factor $8$ out of $8 x - 1200 \cdot 5$ .

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Step 1.2.8.1.1

Factor $8$ out of $8 x$ .

$y = - \frac{8 (x) - 1200 \cdot 5}{5}$

Step 1.2.8.1.2

Factor $8$ out of $- 1200 \cdot 5$ .

$y = - \frac{8 (x) + 8 (- 150 \cdot 5)}{5}$

Step 1.2.8.1.3

Factor $8$ out of $8 (x) + 8 (- 150 \cdot 5)$ .

$y = - \frac{8 (x - 150 \cdot 5)}{5}$

Step 1.2.8.2

Multiply $- 150$ by $5$ .

$y = - \frac{8 (x - 750)}{5}$

Step 1.2.9

Reorder terms.

$y = - (\frac{8}{5} (x - 750))$

Step 1.2.10

Remove parentheses.

$y = - \frac{8}{5} (x - 750)$

Step 2

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

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Step 2.1

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

$m = - \frac{8}{5}$

$b = 0$

Step 2.2

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

Slope: $- \frac{8}{5}$

y-intercept: $(0, 0)$

Slope: $- \frac{8}{5}$

y-intercept: $(0, 0)$

Step 3

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 3.1

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

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Step 3.1.1

Apply the distributive property.

$y = - \frac{8 x + 8 \cdot - 750}{5}$

Step 3.1.2

Multiply $8$ by $- 750$ .

$y = - \frac{8 x - 6000}{5}$

Step 3.1.3

Split the fraction $\frac{8 x - 6000}{5}$ into two fractions.

$y = - (\frac{8 x}{5} + \frac{- 6000}{5})$

Step 3.1.4

Divide $- 6000$ by $5$ .

$y = - (\frac{8 x}{5} - 1200)$

Step 3.1.5

To write $- 1200$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - (\frac{8 x}{5} - 1200 \cdot \frac{5}{5})$

Step 3.1.6

Combine $- 1200$ and $\frac{5}{5}$ .

$y = - (\frac{8 x}{5} + \frac{- 1200 \cdot 5}{5})$

Step 3.1.7

Combine the numerators over the common denominator.

$y = - \frac{8 x - 1200 \cdot 5}{5}$

Step 3.1.8

Simplify the numerator.

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Step 3.1.8.1

Factor $8$ out of $8 x - 1200 \cdot 5$ .

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Step 3.1.8.1.1

Factor $8$ out of $8 x$ .

$y = - \frac{8 (x) - 1200 \cdot 5}{5}$

Step 3.1.8.1.2

Factor $8$ out of $- 1200 \cdot 5$ .

$y = - \frac{8 (x) + 8 (- 150 \cdot 5)}{5}$

Step 3.1.8.1.3

Factor $8$ out of $8 (x) + 8 (- 150 \cdot 5)$ .

$y = - \frac{8 (x - 150 \cdot 5)}{5}$

Step 3.1.8.2

Multiply $- 150$ by $5$ .

$y = - \frac{8 (x - 750)}{5}$

Step 3.1.9

Reorder terms.

$y = - (\frac{8}{5} (x - 750))$

Step 3.1.10

Remove parentheses.

$y = - \frac{8}{5} (x - 750)$

Step 3.2

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

$\begin{array}{c} x & y \\ 0 & 1200 \\ 5 & 1192 \end{array}$

Step 4

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

Slope: $- \frac{8}{5}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 1200 \\ 5 & 1192 \end{array}$

Step 5