Trigonometry Examples

$4 x + 2 y + 2 = 24$

Step 1

Solve for $y$ .

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Step 1.1

Move all terms not containing $y$ to the right side of the equation.

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Step 1.1.1

Subtract $4 x$ from both sides of the equation.

$2 y + 2 = 24 - 4 x$

Step 1.1.2

Subtract $2$ from both sides of the equation.

$2 y = 24 - 4 x - 2$

Step 1.1.3

Subtract $2$ from $24$ .

$2 y = - 4 x + 22$

Step 1.2

Divide each term in $2 y = - 4 x + 22$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y = - 4 x + 22$ by $2$ .

$\frac{2 y}{2} = \frac{- 4 x}{2} + \frac{22}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 4 x}{2} + \frac{22}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4 x}{2} + \frac{22}{2}$

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

Cancel the common factor of $- 4$ and $2$ .

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Step 1.2.3.1.1.1

Factor $2$ out of $- 4 x$ .

$y = \frac{2 (- 2 x)}{2} + \frac{22}{2}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (- 2 x)}{2 (1)} + \frac{22}{2}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (- 2 x)}{2 \cdot 1} + \frac{22}{2}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 2 x}{1} + \frac{22}{2}$

Step 1.2.3.1.1.2.4

Divide $- 2 x$ by $1$ .

$y = - 2 x + \frac{22}{2}$

Step 1.2.3.1.2

Divide $22$ by $2$ .

$y = - 2 x + 11$

Step 2

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

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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

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

$m = - 2$

$b = 11$

Step 2.3

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

Slope: $- 2$

y-intercept: $(0, 11)$

Slope: $- 2$

y-intercept: $(0, 11)$

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

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

$\begin{array}{c} x & y \\ 0 & 11 \\ 1 & 9 \end{array}$

Step 4

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

Slope: $- 2$

y-intercept: $(0, 11)$

$\begin{array}{c} x & y \\ 0 & 11 \\ 1 & 9 \end{array}$

Step 5