Pre-Algebra Examples

$x + 4 y = - 6$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $x$ from both sides of the equation.

$4 y = - 6 - x$

Step 1.2

Divide each term in $4 y = - 6 - x$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 y = - 6 - x$ by $4$ .

$\frac{4 y}{4} = \frac{- 6}{4} + \frac{- x}{4}$

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.

$\frac{4 y}{4} = \frac{- 6}{4} + \frac{- x}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6}{4} + \frac{- x}{4}$

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 $- 6$ and $4$ .

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Step 1.2.3.1.1.1

Factor $2$ out of $- 6$ .

$y = \frac{2 (- 3)}{4} + \frac{- x}{4}$

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 $4$ .

$y = \frac{2 \cdot - 3}{2 \cdot 2} + \frac{- x}{4}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot - 3}{2 \cdot 2} + \frac{- x}{4}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 3}{2} + \frac{- x}{4}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{- x}{4}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = - \frac{3}{2} - \frac{x}{4}$

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 $- \frac{3}{2}$ and $- \frac{x}{4}$ .

$y = - \frac{x}{4} - \frac{3}{2}$

Step 2.3

Write in $y = m x + b$ form.

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Step 2.3.1

Reorder terms.

$y = - (\frac{1}{4} x) - \frac{3}{2}$

Step 2.3.2

Remove parentheses.

$y = - \frac{1}{4} x - \frac{3}{2}$

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 $y = m x + b$ .

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

$b = - \frac{3}{2}$

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: $(0, - \frac{3}{2})$

Slope: $- \frac{1}{4}$

y-intercept: $(0, - \frac{3}{2})$

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 $- \frac{3}{2}$ and $- \frac{x}{4}$ .

$y = - \frac{x}{4} - \frac{3}{2}$

Step 4.1.2

Reorder terms.

$y = - (\frac{1}{4} x) - \frac{3}{2}$

Step 4.1.3

Remove parentheses.

$y = - \frac{1}{4} x - \frac{3}{2}$

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 $x$ .

$0 = - \frac{1}{4} x - \frac{3}{2}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $- \frac{1}{4} x - \frac{3}{2} = 0$ .

$- \frac{1}{4} x - \frac{3}{2} = 0$

Step 4.2.2.2

Combine $x$ and $\frac{1}{4}$ .

$- \frac{x}{4} - \frac{3}{2} = 0$

Step 4.2.2.3

Add $\frac{3}{2}$ to both sides of the equation.

$- \frac{x}{4} = \frac{3}{2}$

Step 4.2.2.4

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{x}{4}) = - 4 (\frac{3}{2})$

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

Simplify $- 4 (- \frac{x}{4})$ .

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Step 4.2.2.5.1.1.1

Cancel the common factor of $4$ .

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Step 4.2.2.5.1.1.1.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$- 4 \frac{- x}{4} = - 4 (\frac{3}{2})$

Step 4.2.2.5.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (\frac{3}{2})$

Step 4.2.2.5.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (\frac{3}{2})$

Step 4.2.2.5.1.1.1.4

Rewrite the expression.

$- - x = - 4 (\frac{3}{2})$

Step 4.2.2.5.1.1.2

Multiply.

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Step 4.2.2.5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (\frac{3}{2})$

Step 4.2.2.5.1.1.2.2

Multiply $x$ by $1$ .

$x = - 4 (\frac{3}{2})$

Step 4.2.2.5.2

Simplify the right side.

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Step 4.2.2.5.2.1

Simplify $- 4 (\frac{3}{2})$ .

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Step 4.2.2.5.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.2.5.2.1.1.1

Factor $2$ out of $- 4$ .

$x = 2 (- 2) \frac{3}{2}$

Step 4.2.2.5.2.1.1.2

Cancel the common factor.

$x = 2 \cdot - 2 \frac{3}{2}$

Step 4.2.2.5.2.1.1.3

Rewrite the expression.

$x = - 2 \cdot 3$

Step 4.2.2.5.2.1.2

Multiply $- 2$ by $3$ .

$x = - 6$

Step 4.2.3

x-intercept(s) in point form.

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

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 $y$ .

$y = - \frac{1}{4} \cdot 0 - \frac{3}{2}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

$y = - \frac{1}{4} \cdot 0 - \frac{3}{2}$

Step 4.3.2.2

Simplify $- \frac{1}{4} \cdot 0 - \frac{3}{2}$ .

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Step 4.3.2.2.1

Multiply $- \frac{1}{4} \cdot 0$ .

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Step 4.3.2.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{4}) - \frac{3}{2}$

Step 4.3.2.2.1.2

Multiply $0$ by $\frac{1}{4}$ .

$y = 0 - \frac{3}{2}$

Step 4.3.2.2.2

Subtract $\frac{3}{2}$ from $0$ .

$y = - \frac{3}{2}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{2})$

Step 4.4

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ - 6 & 0 \\ 0 & - \frac{3}{2} \end{array}$

Step 5

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

Slope: $- \frac{1}{4}$

y-intercept: $(0, - \frac{3}{2})$

$\begin{array}{c} x & y \\ - 6 & 0 \\ 0 & - \frac{3}{2} \end{array}$

Step 6