Pre-Algebra Examples

x - 4 y = 2

$x - 4 y = 2$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

$x$ from both sides of the equation.

$- 4 y = 2 - x$

Step 1.2

Divide each term in

$- 4 y = 2 - x$ by

$- 4$ and simplify.

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Step 1.2.1

Divide each term in

$- 4 y = 2 - x$ by

$- 4$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

$- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide

$y$ by

$1$ .

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

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

$2$ and

$- 4$ .

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Step 1.2.3.1.1.1

Factor

$2$ out of

$2$ .

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

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

$- 4$ .

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

Step 1.2.3.1.1.2.2

Cancel the common factor.

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

Step 1.2.3.1.1.2.3

Rewrite the expression.

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

Step 1.2.3.1.2

Move the negative in front of the fraction.

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

Step 1.2.3.1.3

Dividing two negative values results in a positive value.

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

Step 2

Rewrite in slope-intercept form.

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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

Reorder

$- \frac{1}{2}$ and

$\frac{x}{4}$ .

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

Step 2.3

Reorder terms.

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

Step 3

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

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Step 3.1

Find the values of

$m$ and

$b$ using the form

$y = m x + b$ .

$m = \frac{1}{4}$

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

Step 3.2

The slope of the line is the value of

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

$b$ .

Slope:

$\frac{1}{4}$

y-intercept:

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

Slope:

$\frac{1}{4}$

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.

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Step 4.1

Write in

$y = m x + b$ form.

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Step 4.1.1

Reorder

$- \frac{1}{2}$ and

$\frac{x}{4}$ .

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

Step 4.1.2

Reorder terms.

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

Step 4.2

Find the x-intercept.

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Step 4.2.1

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

$0$ for

$y$ and solve for

$x$ .

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

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as

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

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

Step 4.2.2.2

Combine

$\frac{1}{4}$ and

$x$ .

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

Step 4.2.2.3

Add

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

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

Step 4.2.2.4

Multiply both sides of the equation by

$4$ .

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

Step 4.2.2.5

Simplify both sides of the equation.

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Step 4.2.2.5.1

Simplify the left side.

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Step 4.2.2.5.1.1

Cancel the common factor of

$4$ .

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Step 4.2.2.5.1.1.1

Cancel the common factor.

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

Step 4.2.2.5.1.1.2

Rewrite the expression.

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

Step 4.2.2.5.2

Simplify the right side.

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Step 4.2.2.5.2.1

Cancel the common factor of

$2$ .

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Step 4.2.2.5.2.1.1

Factor

$2$ out of

$4$ .

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

Step 4.2.2.5.2.1.2

Cancel the common factor.

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

Step 4.2.2.5.2.1.3

Rewrite the expression.

$x = 2$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s):

$(2, 0)$

x-intercept(s):

$(2, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

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

$0$ for

$x$ and solve for

$y$ .

$y = \frac{1}{4} \cdot (0) - \frac{1}{2}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Multiply

$\frac{1}{4}$ by

$0$ .

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

Step 4.3.2.2

Remove parentheses.

$y = \frac{1}{4} \cdot (0) - \frac{1}{2}$

Step 4.3.2.3

Simplify

$\frac{1}{4} \cdot (0) - \frac{1}{2}$ .

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Step 4.3.2.3.1

Multiply

$\frac{1}{4}$ by

$0$ .

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

Step 4.3.2.3.2

Subtract

$\frac{1}{2}$ from

$0$ .

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

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.

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

Step 5

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

Slope:

$\frac{1}{4}$

y-intercept:

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

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

Step 6