Pre-Algebra Examples

$128 = (2 l + 4) + 2 w$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $2 y + 4 + 2 x = 128$ .

$2 y + 4 + 2 x = 128$

Step 1.2

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Subtract $4$ from both sides of the equation.

$2 y + 2 x = 128 - 4$

Step 1.2.2

Subtract $2 x$ from both sides of the equation.

$2 y = 128 - 4 - 2 x$

Step 1.2.3

Subtract $4$ from $128$ .

$2 y = 124 - 2 x$

Step 1.3

Divide each term in $2 y = 124 - 2 x$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 y = 124 - 2 x$ by $2$ .

$\frac{2 y}{2} = \frac{124}{2} + \frac{- 2 x}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{124}{2} + \frac{- 2 x}{2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{124}{2} + \frac{- 2 x}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $124$ by $2$ .

$y = 62 + \frac{- 2 x}{2}$

Step 1.3.3.1.2

Cancel the common factor of $- 2$ and $2$ .

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Step 1.3.3.1.2.1

Factor $2$ out of $- 2 x$ .

$y = 62 + \frac{2 (- x)}{2}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $2$ out of $2$ .

$y = 62 + \frac{2 (- x)}{2 (1)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = 62 + \frac{2 (- x)}{2 \cdot 1}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = 62 + \frac{- x}{1}$

Step 1.3.3.1.2.2.4

Divide $- x$ by $1$ .

$y = 62 - x$

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 $62$ and $- x$ .

$y = - x + 62$

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 $y = m x + b$ .

$m = - 1$

$b = 62$

Step 3.2

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

Slope: $- 1$

y-intercept: $(0, 62)$

Slope: $- 1$

y-intercept: $(0, 62)$

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

Reorder $62$ and $- x$ .

$y = - x + 62$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 62 \\ 1 & 61 \end{array}$

Step 5

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

Slope: $- 1$

y-intercept: $(0, 62)$

$\begin{array}{c} x & y \\ 0 & 62 \\ 1 & 61 \end{array}$

Step 6