Pre-Algebra Examples

$10 x - 20 y + 12 = 0$

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 $10 x$ from both sides of the equation.

$- 20 y + 12 = - 10 x$

Step 1.1.2

Subtract $12$ from both sides of the equation.

$- 20 y = - 10 x - 12$

Step 1.2

Divide each term in $- 20 y = - 10 x - 12$ by $- 20$ and simplify.

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Step 1.2.1

Divide each term in $- 20 y = - 10 x - 12$ by $- 20$ .

$\frac{- 20 y}{- 20} = \frac{- 10 x}{- 20} + \frac{- 12}{- 20}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 20$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 20 y}{- 20} = \frac{- 10 x}{- 20} + \frac{- 12}{- 20}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 10 x}{- 20} + \frac{- 12}{- 20}$

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 $- 10$ and $- 20$ .

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Step 1.2.3.1.1.1

Factor $- 10$ out of $- 10 x$ .

$y = \frac{- 10 (x)}{- 20} + \frac{- 12}{- 20}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $- 10$ out of $- 20$ .

$y = \frac{- 10 (x)}{- 10 (2)} + \frac{- 12}{- 20}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 10 x}{- 10 \cdot 2} + \frac{- 12}{- 20}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{- 12}{- 20}$

Step 1.2.3.1.2

Cancel the common factor of $- 12$ and $- 20$ .

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Step 1.2.3.1.2.1

Factor $- 4$ out of $- 12$ .

$y = \frac{x}{2} + \frac{- 4 (3)}{- 20}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $- 4$ out of $- 20$ .

$y = \frac{x}{2} + \frac{- 4 \cdot 3}{- 4 \cdot 5}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{x}{2} + \frac{- 4 \cdot 3}{- 4 \cdot 5}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{3}{5}$

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 terms.

$y = \frac{1}{2} x + \frac{3}{5}$

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 $y = m x + b$ .

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

$b = \frac{3}{5}$

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: $(0, \frac{3}{5})$

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

y-intercept: $(0, \frac{3}{5})$

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 terms.

$y = \frac{1}{2} x + \frac{3}{5}$

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 $x$ .

$0 = \frac{1}{2} x + \frac{3}{5}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $\frac{1}{2} x + \frac{3}{5} = 0$ .

$\frac{1}{2} x + \frac{3}{5} = 0$

Step 4.2.2.2

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

$\frac{x}{2} + \frac{3}{5} = 0$

Step 4.2.2.3

Subtract $\frac{3}{5}$ from both sides of the equation.

$\frac{x}{2} = - \frac{3}{5}$

Step 4.2.2.4

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (- \frac{3}{5})$

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

Cancel the common factor of $2$ .

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Step 4.2.2.5.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (- \frac{3}{5})$

Step 4.2.2.5.1.1.2

Rewrite the expression.

$x = 2 (- \frac{3}{5})$

Step 4.2.2.5.2

Simplify the right side.

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Step 4.2.2.5.2.1

Simplify $2 (- \frac{3}{5})$ .

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Step 4.2.2.5.2.1.1

Multiply $2 (- \frac{3}{5})$ .

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Step 4.2.2.5.2.1.1.1

Multiply $- 1$ by $2$ .

$x = - 2 (\frac{3}{5})$

Step 4.2.2.5.2.1.1.2

Combine $- 2$ and $\frac{3}{5}$ .

$x = \frac{- 2 \cdot 3}{5}$

Step 4.2.2.5.2.1.1.3

Multiply $- 2$ by $3$ .

$x = \frac{- 6}{5}$

Step 4.2.2.5.2.1.2

Move the negative in front of the fraction.

$x = - \frac{6}{5}$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{6}{5}, 0)$

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 $y$ .

$y = \frac{1}{2} \cdot (0) + \frac{3}{5}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

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

$y = \frac{1}{2} \cdot 0 + \frac{3}{5}$

Step 4.3.2.2

Remove parentheses.

$y = \frac{1}{2} \cdot (0) + \frac{3}{5}$

Step 4.3.2.3

Simplify $\frac{1}{2} \cdot (0) + \frac{3}{5}$ .

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Step 4.3.2.3.1

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

$y = 0 + \frac{3}{5}$

Step 4.3.2.3.2

Add $0$ and $\frac{3}{5}$ .

$y = \frac{3}{5}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{5})$

Step 4.4

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

$\begin{array}{c} x & y \\ - \frac{6}{5} & 0 \\ 0 & \frac{3}{5} \end{array}$

Step 5

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

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

y-intercept: $(0, \frac{3}{5})$

$\begin{array}{c} x & y \\ - \frac{6}{5} & 0 \\ 0 & \frac{3}{5} \end{array}$

Step 6