Pre-Algebra Examples

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

Step 1

Solve for $y$ .

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Step 1.1

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

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

Step 1.2

Multiply both sides of the equation by $3$ .

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

Step 1.3

Simplify the left side.

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Step 1.3.1

Cancel the common factor of $3$ .

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Step 1.3.1.1

Cancel the common factor.

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

Step 1.3.1.2

Rewrite the expression.

$y = 3 x$

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 $y = m x + b$ .

$m = 3$

$b = 0$

Step 2.3

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

Slope: $3$

y-intercept: $(0, 0)$

Slope: $3$

y-intercept: $(0, 0)$

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.

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 3 \end{array}$

Step 4

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

Slope: $3$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 3 \end{array}$

Step 5