Trigonometry Examples

x - 8 y = - 4

$x - 8 y = - 4$

Step 1

Solve for

y

$y$ .

Tap for more steps...

Step 1.1

Subtract

x

$x$ from both sides of the equation.

- 8 y = - 4 - x

$- 8 y = - 4 - x$

Step 1.2

Divide each term in

- 8 y = - 4 - x

$- 8 y = - 4 - x$ by

- 8

$- 8$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in

- 8 y = - 4 - x

$- 8 y = - 4 - x$ by

- 8

$- 8$ .

\frac{- 8 y}{- 8} = \frac{- 4}{- 8} + \frac{- x}{- 8}

$\frac{- 8 y}{- 8} = \frac{- 4}{- 8} + \frac{- x}{- 8}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of

- 8

$- 8$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 4}{- 8} + \frac{- x}{- 8}$

Step 1.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{- 4}{- 8} + \frac{- x}{- 8}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Cancel the common factor of

$- 4$ and

$- 8$ .

Tap for more steps...

Step 1.2.3.1.1.1

Factor

$- 4$ out of

$- 4$ .

$y = \frac{- 4 (1)}{- 8} + \frac{- x}{- 8}$

Step 1.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.1.2.1

Factor

$- 4$ out of

$- 8$ .

$y = \frac{- 4 \cdot 1}{- 4 \cdot 2} + \frac{- x}{- 8}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 4 \cdot 1}{- 4 \cdot 2} + \frac{- x}{- 8}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{1}{2} + \frac{- x}{- 8}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{1}{2} + \frac{x}{8}$

Step 2

Rewrite in slope-intercept form.

Tap for more steps...

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

$\frac{1}{2}$ and

$\frac{x}{8}$ .

$y = \frac{x}{8} + \frac{1}{2}$

Step 2.3

Reorder terms.

$y = \frac{1}{8} x + \frac{1}{2}$

Step 3

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

Tap for more steps...

Step 3.1

Find the values of

$m$ and

$b$ using the form

$y = m x + b$ .

$m = \frac{1}{8}$

$b = \frac{1}{2}$

Step 3.2

The slope of the line is the value of

$m$ , and the y-intercept is the value of

$b$ .

Slope:

$\frac{1}{8}$

y-intercept:

$(0, \frac{1}{2})$

Slope:

$\frac{1}{8}$

y-intercept:

$(0, \frac{1}{2})$

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.

Tap for more steps...

Step 4.1

Write in

$y = m x + b$ form.

Tap for more steps...

Step 4.1.1

Reorder

$\frac{1}{2}$ and

$\frac{x}{8}$ .

$y = \frac{x}{8} + \frac{1}{2}$

Step 4.1.2

Reorder terms.

$y = \frac{1}{8} x + \frac{1}{2}$

Step 4.2

Find the x-intercept.

Tap for more steps...

Step 4.2.1

To find the x-intercept(s), substitute in

$0$ for

$y$ and solve for

$x$ .

$0 = \frac{1}{8} x + \frac{1}{2}$

Step 4.2.2

Solve the equation.

Tap for more steps...

Step 4.2.2.1

Rewrite the equation as

$\frac{1}{8} x + \frac{1}{2} = 0$ .

$\frac{1}{8} x + \frac{1}{2} = 0$

Step 4.2.2.2

Combine

$\frac{1}{8}$ and

$x$ .

$\frac{x}{8} + \frac{1}{2} = 0$

Step 4.2.2.3

Subtract

$\frac{1}{2}$ from both sides of the equation.

$\frac{x}{8} = - \frac{1}{2}$

Step 4.2.2.4

Multiply both sides of the equation by

$8$ .

$8 \frac{x}{8} = 8 (- \frac{1}{2})$

Step 4.2.2.5

Simplify both sides of the equation.

Tap for more steps...

Step 4.2.2.5.1

Simplify the left side.

Tap for more steps...

Step 4.2.2.5.1.1

Cancel the common factor of

$8$ .

Tap for more steps...

Step 4.2.2.5.1.1.1

Cancel the common factor.

$8 \frac{x}{8} = 8 (- \frac{1}{2})$

Step 4.2.2.5.1.1.2

Rewrite the expression.

$x = 8 (- \frac{1}{2})$

Step 4.2.2.5.2

Simplify the right side.

Tap for more steps...

Step 4.2.2.5.2.1

Simplify

$8 (- \frac{1}{2})$ .

Tap for more steps...

Step 4.2.2.5.2.1.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 4.2.2.5.2.1.1.1

Move the leading negative in

$- \frac{1}{2}$ into the numerator.

$x = 8 (\frac{- 1}{2})$

Step 4.2.2.5.2.1.1.2

Factor

$2$ out of

$8$ .

$x = 2 (4) \frac{- 1}{2}$

Step 4.2.2.5.2.1.1.3

Cancel the common factor.

$x = 2 \cdot 4 \frac{- 1}{2}$

Step 4.2.2.5.2.1.1.4

Rewrite the expression.

$x = 4 \cdot - 1$

Step 4.2.2.5.2.1.2

Multiply

$4$ by

$- 1$ .

$x = - 4$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s):

$(- 4, 0)$

x-intercept(s):

$(- 4, 0)$

Step 4.3

Find the y-intercept.

Tap for more steps...

Step 4.3.1

To find the y-intercept(s), substitute in

$0$ for

$x$ and solve for

$y$ .

$y = \frac{1}{8} \cdot (0) + \frac{1}{2}$

Step 4.3.2

Solve the equation.

Tap for more steps...

Step 4.3.2.1

Multiply

$\frac{1}{8}$ by

$0$ .

$y = \frac{1}{8} \cdot 0 + \frac{1}{2}$

Step 4.3.2.2

Remove parentheses.

$y = \frac{1}{8} \cdot (0) + \frac{1}{2}$

Step 4.3.2.3

Simplify

$\frac{1}{8} \cdot (0) + \frac{1}{2}$ .

Tap for more steps...

Step 4.3.2.3.1

Multiply

$\frac{1}{8}$ by

$0$ .

$y = 0 + \frac{1}{2}$

Step 4.3.2.3.2

Add

$0$ and

$\frac{1}{2}$ .

$y = \frac{1}{2}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s):

$(0, \frac{1}{2})$

y-intercept(s):

$(0, \frac{1}{2})$

Step 4.4

Create a table of the

$x$ and

$y$ values.

$\begin{array}{c} x & y \\ - 4 & 0 \\ 0 & \frac{1}{2} \end{array}$

Step 5

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

Slope:

$\frac{1}{8}$

y-intercept:

$(0, \frac{1}{2})$

$\begin{array}{c} x & y \\ - 4 & 0 \\ 0 & \frac{1}{2} \end{array}$

Step 6