Pre-Algebra Examples

$(x + 4) \cdot 2 + (y - 3) \cdot 2 = 25$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

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

$2 y + 2 = 25 - 2 x$

Step 1.1.2

Subtract $2$ from both sides of the equation.

$2 y = 25 - 2 x - 2$

Step 1.1.3

Subtract $2$ from $25$ .

$2 y = - 2 x + 23$

Step 1.2

Divide each term in $2 y = - 2 x + 23$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y = - 2 x + 23$ by $2$ .

$\frac{2 y}{2} = \frac{- 2 x}{2} + \frac{23}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2 x}{2} + \frac{23}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 2 x}{2} + \frac{23}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

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

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Step 1.2.3.1.1

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

$y = \frac{2 (- x)}{2} + \frac{23}{2}$

Step 1.2.3.1.2

Cancel the common factors.

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Step 1.2.3.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (- x)}{2 (1)} + \frac{23}{2}$

Step 1.2.3.1.2.2

Cancel the common factor.

$y = \frac{2 (- x)}{2 \cdot 1} + \frac{23}{2}$

Step 1.2.3.1.2.3

Rewrite the expression.

$y = \frac{- x}{1} + \frac{23}{2}$

Step 1.2.3.1.2.4

Divide $- x$ by $1$ .

$y = - x + \frac{23}{2}$

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 $y = m x + b$ .

$m = - 1$

$b = \frac{23}{2}$

Step 2.3

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

Slope: $- 1$

y-intercept: $(0, \frac{23}{2})$

Slope: $- 1$

y-intercept: $(0, \frac{23}{2})$

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

Find the x-intercept.

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Step 3.1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - x + \frac{23}{2}$

Step 3.1.2

Solve the equation.

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Step 3.1.2.1

Rewrite the equation as $- x + \frac{23}{2} = 0$ .

$- x + \frac{23}{2} = 0$

Step 3.1.2.2

Subtract $\frac{23}{2}$ from both sides of the equation.

$- x = - \frac{23}{2}$

Step 3.1.2.3

Divide each term in $- x = - \frac{23}{2}$ by $- 1$ and simplify.

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Step 3.1.2.3.1

Divide each term in $- x = - \frac{23}{2}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \frac{23}{2}}{- 1}$

Step 3.1.2.3.2

Simplify the left side.

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Step 3.1.2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \frac{23}{2}}{- 1}$

Step 3.1.2.3.2.2

Divide $x$ by $1$ .

$x = \frac{- \frac{23}{2}}{- 1}$

Step 3.1.2.3.3

Simplify the right side.

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Step 3.1.2.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{\frac{23}{2}}{1}$

Step 3.1.2.3.3.2

Divide $\frac{23}{2}$ by $1$ .

$x = \frac{23}{2}$

Step 3.1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{23}{2}, 0)$

Step 3.2

Find the y-intercept.

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Step 3.2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - (0) + \frac{23}{2}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Remove parentheses.

$y = - (0) + \frac{23}{2}$

Step 3.2.2.2

Simplify $- (0) + \frac{23}{2}$ .

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Step 3.2.2.2.1

Multiply $- 1$ by $0$ .

$y = 0 + \frac{23}{2}$

Step 3.2.2.2.2

Add $0$ and $\frac{23}{2}$ .

$y = \frac{23}{2}$

Step 3.2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{23}{2})$

Step 3.3

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

$\begin{array}{c} x & y \\ 0 & \frac{23}{2} \\ \frac{23}{2} & 0 \end{array}$

Step 4

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

Slope: $- 1$

y-intercept: $(0, \frac{23}{2})$

$\begin{array}{c} x & y \\ 0 & \frac{23}{2} \\ \frac{23}{2} & 0 \end{array}$

Step 5