Trigonometry Examples

2 x + 4 y = 5

$2 x + 4 y = 5$

Step 1

Solve for

y

$y$ .

Tap for more steps...

Step 1.1

Subtract

2 x

$2 x$ from both sides of the equation.

4 y = 5 - 2 x

$4 y = 5 - 2 x$

Step 1.2

Divide each term in

4 y = 5 - 2 x

$4 y = 5 - 2 x$ by

4

$4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in

4 y = 5 - 2 x

$4 y = 5 - 2 x$ by

4

$4$ .

\frac{4 y}{4} = \frac{5}{4} + \frac{- 2 x}{4}

$\frac{4 y}{4} = \frac{5}{4} + \frac{- 2 x}{4}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of

4

$4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{5}{4} + \frac{- 2 x}{4}$

Step 1.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{5}{4} + \frac{- 2 x}{4}$

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

$- 2$ and

$4$ .

Tap for more steps...

Step 1.2.3.1.1.1

Factor

$2$ out of

$- 2 x$ .

$y = \frac{5}{4} + \frac{2 (- x)}{4}$

Step 1.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.1.2.1

Factor

$2$ out of

$4$ .

$y = \frac{5}{4} + \frac{2 (- x)}{2 (2)}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{5}{4} + \frac{2 (- x)}{2 \cdot 2}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{5}{4} + \frac{- x}{2}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = \frac{5}{4} - \frac{x}{2}$

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

$\frac{5}{4}$ and

$- \frac{x}{2}$ .

$y = - \frac{x}{2} + \frac{5}{4}$

Step 2.3

Write in

$y = m x + b$ form.

Tap for more steps...

Step 2.3.1

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{5}{4}$

Step 2.3.2

Remove parentheses.

$y = - \frac{1}{2} x + \frac{5}{4}$

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

$y = m x + b$ .

$m = - \frac{1}{2}$

$b = \frac{5}{4}$

Step 3.2

The slope of the line is the value of

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

$b$ .

Slope:

$- \frac{1}{2}$

y-intercept:

$(0, \frac{5}{4})$

Slope:

$- \frac{1}{2}$

y-intercept:

$(0, \frac{5}{4})$

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

$\frac{5}{4}$ and

$- \frac{x}{2}$ .

$y = - \frac{x}{2} + \frac{5}{4}$

Step 4.1.2

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{5}{4}$

Step 4.1.3

Remove parentheses.

$y = - \frac{1}{2} x + \frac{5}{4}$

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

$x$ .

$0 = - \frac{1}{2} x + \frac{5}{4}$

Step 4.2.2

Solve the equation.

Tap for more steps...

Step 4.2.2.1

Rewrite the equation as

$- \frac{1}{2} x + \frac{5}{4} = 0$ .

$- \frac{1}{2} x + \frac{5}{4} = 0$

Step 4.2.2.2

Combine

$x$ and

$\frac{1}{2}$ .

$- \frac{x}{2} + \frac{5}{4} = 0$

Step 4.2.2.3

Subtract

$\frac{5}{4}$ from both sides of the equation.

$- \frac{x}{2} = - \frac{5}{4}$

Step 4.2.2.4

Multiply both sides of the equation by

$- 2$ .

$- 2 (- \frac{x}{2}) = - 2 (- \frac{5}{4})$

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

Simplify

$- 2 (- \frac{x}{2})$ .

Tap for more steps...

Step 4.2.2.5.1.1.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 4.2.2.5.1.1.1.1

Move the leading negative in

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

$- 2 \frac{- x}{2} = - 2 (- \frac{5}{4})$

Step 4.2.2.5.1.1.1.2

Factor

$2$ out of

$- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 (- \frac{5}{4})$

Step 4.2.2.5.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 (- \frac{5}{4})$

Step 4.2.2.5.1.1.1.4

Rewrite the expression.

$- - x = - 2 (- \frac{5}{4})$

Step 4.2.2.5.1.1.2

Multiply.

Tap for more steps...

Step 4.2.2.5.1.1.2.1

Multiply

$- 1$ by

$- 1$ .

$1 x = - 2 (- \frac{5}{4})$

Step 4.2.2.5.1.1.2.2

Multiply

$x$ by

$1$ .

$x = - 2 (- \frac{5}{4})$

Step 4.2.2.5.2

Simplify the right side.

Tap for more steps...

Step 4.2.2.5.2.1

Simplify

$- 2 (- \frac{5}{4})$ .

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

$- \frac{5}{4}$ into the numerator.

$x = - 2 (\frac{- 5}{4})$

Step 4.2.2.5.2.1.1.2

Factor

$2$ out of

$- 2$ .

$x = 2 (- 1) \frac{- 5}{4}$

Step 4.2.2.5.2.1.1.3

Factor

$2$ out of

$4$ .

$x = 2 \cdot - 1 \frac{- 5}{2 \cdot 2}$

Step 4.2.2.5.2.1.1.4

Cancel the common factor.

$x = 2 \cdot - 1 \frac{- 5}{2 \cdot 2}$

Step 4.2.2.5.2.1.1.5

Rewrite the expression.

$x = - \frac{- 5}{2}$

Step 4.2.2.5.2.1.2

Move the negative in front of the fraction.

$x = - - \frac{5}{2}$

Step 4.2.2.5.2.1.3

Multiply

$- - \frac{5}{2}$ .

Tap for more steps...

Step 4.2.2.5.2.1.3.1

Multiply

$- 1$ by

$- 1$ .

$x = 1 (\frac{5}{2})$

Step 4.2.2.5.2.1.3.2

Multiply

$\frac{5}{2}$ by

$1$ .

$x = \frac{5}{2}$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s):

$(\frac{5}{2}, 0)$

x-intercept(s):

$(\frac{5}{2}, 0)$

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

$y$ .

$y = - \frac{1}{2} \cdot 0 + \frac{5}{4}$

Step 4.3.2

Solve the equation.

Tap for more steps...

Step 4.3.2.1

Remove parentheses.

$y = - \frac{1}{2} \cdot 0 + \frac{5}{4}$

Step 4.3.2.2

Simplify

$- \frac{1}{2} \cdot 0 + \frac{5}{4}$ .

Tap for more steps...

Step 4.3.2.2.1

Multiply

$- \frac{1}{2} \cdot 0$ .

Tap for more steps...

Step 4.3.2.2.1.1

Multiply

$0$ by

$- 1$ .

$y = 0 (\frac{1}{2}) + \frac{5}{4}$

Step 4.3.2.2.1.2

Multiply

$0$ by

$\frac{1}{2}$ .

$y = 0 + \frac{5}{4}$

Step 4.3.2.2.2

Add

$0$ and

$\frac{5}{4}$ .

$y = \frac{5}{4}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s):

$(0, \frac{5}{4})$

y-intercept(s):

$(0, \frac{5}{4})$

Step 4.4

Create a table of the

$x$ and

$y$ values.

$\begin{array}{c} x & y \\ 0 & \frac{5}{4} \\ \frac{5}{2} & 0 \end{array}$

Step 5

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

Slope:

$- \frac{1}{2}$

y-intercept:

$(0, \frac{5}{4})$

$\begin{array}{c} x & y \\ 0 & \frac{5}{4} \\ \frac{5}{2} & 0 \end{array}$

Step 6