Trigonometry Examples

$2 x + 3 y = - 17$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$3 y = - 17 - 2 x$

Step 1.2

Divide each term in $3 y = - 17 - 2 x$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y = - 17 - 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 17}{3} + \frac{- 2 x}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 17}{3} + \frac{- 2 x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 17}{3} + \frac{- 2 x}{3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{17}{3} + \frac{- 2 x}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{17}{3} - \frac{2 x}{3}$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Reorder $- \frac{17}{3}$ and $- \frac{2 x}{3}$ .

$y = - \frac{2 x}{3} - \frac{17}{3}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{2}{3} x) - \frac{17}{3}$

Step 2.3.2

Remove parentheses.

$y = - \frac{2}{3} x - \frac{17}{3}$

Step 3

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

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Step 3.1

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

$m = - \frac{2}{3}$

$b = - \frac{17}{3}$

Step 3.2

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, - \frac{17}{3})$

Slope: $- \frac{2}{3}$

y-intercept: $(0, - \frac{17}{3})$

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

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

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Step 4.1.1

Reorder $- \frac{17}{3}$ and $- \frac{2 x}{3}$ .

$y = - \frac{2 x}{3} - \frac{17}{3}$

Step 4.1.2

Reorder terms.

$y = - (\frac{2}{3} x) - \frac{17}{3}$

Step 4.1.3

Remove parentheses.

$y = - \frac{2}{3} x - \frac{17}{3}$

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 $x$ .

$0 = - \frac{2}{3} x - \frac{17}{3}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $- \frac{2}{3} x - \frac{17}{3} = 0$ .

$- \frac{2}{3} x - \frac{17}{3} = 0$

Step 4.2.2.2

Simplify each term.

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Step 4.2.2.2.1

Combine $x$ and $\frac{2}{3}$ .

$- \frac{x \cdot 2}{3} - \frac{17}{3} = 0$

Step 4.2.2.2.2

Move $2$ to the left of $x$ .

$- \frac{2 x}{3} - \frac{17}{3} = 0$

Step 4.2.2.3

Add $\frac{17}{3}$ to both sides of the equation.

$- \frac{2 x}{3} = \frac{17}{3}$

Step 4.2.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 2 x = 17$

Step 4.2.2.5

Divide each term in $- 2 x = 17$ by $- 2$ and simplify.

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Step 4.2.2.5.1

Divide each term in $- 2 x = 17$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{17}{- 2}$

Step 4.2.2.5.2

Simplify the left side.

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Step 4.2.2.5.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.2.5.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{17}{- 2}$

Step 4.2.2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{17}{- 2}$

Step 4.2.2.5.3

Simplify the right side.

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Step 4.2.2.5.3.1

Move the negative in front of the fraction.

$x = - \frac{17}{2}$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{17}{2}, 0)$

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 $y$ .

$y = - \frac{2}{3} \cdot 0 - \frac{17}{3}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

$y = - \frac{2}{3} \cdot 0 - \frac{17}{3}$

Step 4.3.2.2

Simplify $- \frac{2}{3} \cdot 0 - \frac{17}{3}$ .

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Step 4.3.2.2.1

Multiply $- \frac{2}{3} \cdot 0$ .

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Step 4.3.2.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{2}{3}) - \frac{17}{3}$

Step 4.3.2.2.1.2

Multiply $0$ by $\frac{2}{3}$ .

$y = 0 - \frac{17}{3}$

Step 4.3.2.2.2

Subtract $\frac{17}{3}$ from $0$ .

$y = - \frac{17}{3}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{17}{3})$

Step 4.4

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

$\begin{array}{c} x & y \\ - \frac{17}{2} & 0 \\ 0 & - \frac{17}{3} \end{array}$

Step 5

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, - \frac{17}{3})$

$\begin{array}{c} x & y \\ - \frac{17}{2} & 0 \\ 0 & - \frac{17}{3} \end{array}$

Step 6