Pre-Algebra Examples

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

Step 1

Solve for $y$ .

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Step 1.1

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

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

Step 1.2

Subtract $3$ from both sides of the equation.

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

Step 1.3

Multiply both sides of the equation by $- 2$ .

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

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $- 2 (- \frac{y}{2})$ .

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Step 1.4.1.1.1

Cancel the common factor of $2$ .

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Step 1.4.1.1.1.1

Move the leading negative in $- \frac{y}{2}$ into the numerator.

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

Step 1.4.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 1.4.1.1.1.3

Cancel the common factor.

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

Step 1.4.1.1.1.4

Rewrite the expression.

$- - y = - 2 (x - 3)$

Step 1.4.1.1.2

Multiply.

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Step 1.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 2 (x - 3)$

Step 1.4.1.1.2.2

Multiply $y$ by $1$ .

$y = - 2 (x - 3)$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $- 2 (x - 3)$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y = - 2 x - 2 \cdot - 3$

Step 1.4.2.1.2

Multiply $- 2$ by $- 3$ .

$y = - 2 x + 6$

Step 2

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

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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

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 2$

$b = 6$

Step 2.3

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

Slope: $- 2$

y-intercept: $(0, 6)$

Slope: $- 2$

y-intercept: $(0, 6)$

Step 3

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 3.1

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

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 4 \end{array}$

Step 4

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

Slope: $- 2$

y-intercept: $(0, 6)$

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 4 \end{array}$

Step 5