Trigonometry Examples

$y - 8 = - 4 (x - 3)$

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 $x$ .

$(0) - 8 = - 4 (x - 3)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 4 (x - 3) = (0) - 8$ .

$- 4 (x - 3) = (0) - 8$

Step 1.2.2

Subtract $8$ from $0$ .

$- 4 (x - 3) = - 8$

Step 1.2.3

Divide each term in $- 4 (x - 3) = - 8$ by $- 4$ and simplify.

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Step 1.2.3.1

Divide each term in $- 4 (x - 3) = - 8$ by $- 4$ .

$\frac{- 4 (x - 3)}{- 4} = \frac{- 8}{- 4}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{- 4 (x - 3)}{- 4} = \frac{- 8}{- 4}$

Step 1.2.3.2.1.2

Divide $x - 3$ by $1$ .

$x - 3 = \frac{- 8}{- 4}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 8$ by $- 4$ .

$x - 3 = 2$

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

Add $3$ to both sides of the equation.

$x = 2 + 3$

Step 1.2.4.2

Add $2$ and $3$ .

$x = 5$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(5, 0)$

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 $y$ .

$y - 8 = - 4 ((0) - 3)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $- 4 ((0) - 3)$ .

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Step 2.2.1.1

Subtract $3$ from $0$ .

$y - 8 = - 4 \cdot - 3$

Step 2.2.1.2

Multiply $- 4$ by $- 3$ .

$y - 8 = 12$

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.

$y = 12 + 8$

Step 2.2.2.2

Add $12$ and $8$ .

$y = 20$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 20)$

Step 3

List the intersections.

x-intercept(s): $(5, 0)$

y-intercept(s): $(0, 20)$

Step 4