Pre-Algebra Examples

$6 y + 3 x = 9$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$6 y = 9 - 3 x$

Step 1.2

Divide each term in $6 y = 9 - 3 x$ by $6$ and simplify.

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Step 1.2.1

Divide each term in $6 y = 9 - 3 x$ by $6$ .

$\frac{6 y}{6} = \frac{9}{6} + \frac{- 3 x}{6}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $6$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{9}{6} + \frac{- 3 x}{6}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{6} + \frac{- 3 x}{6}$

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 $9$ and $6$ .

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Step 1.2.3.1.1.1

Factor $3$ out of $9$ .

$y = \frac{3 (3)}{6} + \frac{- 3 x}{6}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $3$ out of $6$ .

$y = \frac{3 \cdot 3}{3 \cdot 2} + \frac{- 3 x}{6}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot 3}{3 \cdot 2} + \frac{- 3 x}{6}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} + \frac{- 3 x}{6}$

Step 1.2.3.1.2

Cancel the common factor of $- 3$ and $6$ .

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Step 1.2.3.1.2.1

Factor $3$ out of $- 3 x$ .

$y = \frac{3}{2} + \frac{3 (- x)}{6}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $3$ out of $6$ .

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

Step 1.2.3.1.2.2.2

Cancel the common factor.

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

Step 1.2.3.1.2.2.3

Rewrite the expression.

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

Step 1.2.3.1.3

Move the negative in front of the fraction.

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

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

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

Step 2.3

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

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Step 2.3.1

Reorder terms.

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

Step 2.3.2

Remove parentheses.

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

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 $y = m x + b$ .

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

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

Step 3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{1}{2}$

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

Slope: $- \frac{1}{2}$

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

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

Step 4.1.2

Reorder terms.

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

Step 4.1.3

Remove parentheses.

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

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 $x$ .

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

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

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

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

Step 4.2.2.2

Combine $x$ and $\frac{1}{2}$ .

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

Step 4.2.2.3

Subtract $\frac{3}{2}$ from both sides of the equation.

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

Step 4.2.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x = - 3$

Step 4.2.2.5

Divide each term in $- x = - 3$ by $- 1$ and simplify.

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Step 4.2.2.5.1

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Step 4.2.2.5.2

Simplify the left side.

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Step 4.2.2.5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Step 4.2.2.5.2.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Step 4.2.2.5.3

Simplify the right side.

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Step 4.2.2.5.3.1

Divide $- 3$ by $- 1$ .

$x = 3$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(3, 0)$

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 $y$ .

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

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

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

Step 4.3.2.2

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

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Step 4.3.2.2.1

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

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Step 4.3.2.2.1.1

Multiply $0$ by $- 1$ .

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

Step 4.3.2.2.1.2

Multiply $0$ by $\frac{1}{2}$ .

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

Step 4.3.2.2.2

Add $0$ and $\frac{3}{2}$ .

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

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.

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

Step 5

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

Slope: $- \frac{1}{2}$

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

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

Step 6