Trigonometry Examples

$y - 8 = 2 (x + 2)$

Step 1

Find the x-intercepts.

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Step 1.1

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

$(0) - 8 = 2 (x + 2)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $2 (x + 2) = (0) - 8$ .

$2 (x + 2) = (0) - 8$

Step 1.2.2

Subtract $8$ from $0$ .

$2 (x + 2) = - 8$

Step 1.2.3

Divide each term in $2 (x + 2) = - 8$ by $2$ and simplify.

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Step 1.2.3.1

Divide each term in $2 (x + 2) = - 8$ by $2$ .

$\frac{2 (x + 2)}{2} = \frac{- 8}{2}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $2$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{2 (x + 2)}{2} = \frac{- 8}{2}$

Step 1.2.3.2.1.2

Divide $x + 2$ by $1$ .

$x + 2 = \frac{- 8}{2}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 8$ by $2$ .

$x + 2 = - 4$

Step 1.2.4

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

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Step 1.2.4.1

Subtract $2$ from both sides of the equation.

$x = - 4 - 2$

Step 1.2.4.2

Subtract $2$ from $- 4$ .

$x = - 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 6, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y - 8 = 2 ((0) + 2)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $2 ((0) + 2)$ .

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Step 2.2.1.1

Add $0$ and $2$ .

$y - 8 = 2 \cdot 2$

Step 2.2.1.2

Multiply $2$ by $2$ .

$y - 8 = 4$

Step 2.2.2

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

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Step 2.2.2.1

Add $8$ to both sides of the equation.

$y = 4 + 8$

Step 2.2.2.2

Add $4$ and $8$ .

$y = 12$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 12)$

Step 3

List the intersections.

x-intercept(s): $(- 6, 0)$

y-intercept(s): $(0, 12)$

Step 4