Algebra Examples

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

Step 1

Solve for $y$ .

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Step 1.1

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Step 1.2

Simplify both sides of the equation.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 1.2.1.1.1

Cancel the common factor of $3$ .

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Step 1.2.1.1.1.1

Cancel the common factor.

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

Step 1.2.1.1.1.2

Rewrite the expression.

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

Step 1.2.1.1.2

Cancel the common factor of $2$ .

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Step 1.2.1.1.2.1

Factor $2$ out of $2 y$ .

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

Step 1.2.1.1.2.2

Cancel the common factor.

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

Step 1.2.1.1.2.3

Rewrite the expression.

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

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

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

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Step 1.2.2.1.1

Multiply $\frac{3}{2}$ by $\frac{x}{2}$ .

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

Step 1.2.2.1.2

Multiply $2$ by $2$ .

$y = - \frac{3 x}{4}$

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

Write in $y = m x + b$ form.

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Step 2.2.1

Reorder terms.

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

Step 2.2.2

Remove parentheses.

$y = - \frac{3}{4} x$

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 $y = m x + b$ .

$m = - \frac{3}{4}$

$b = 0$

Step 3.2

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

Slope: $- \frac{3}{4}$

y-intercept: $(0, 0)$

Slope: $- \frac{3}{4}$

y-intercept: $(0, 0)$

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

Write in $y = m x + b$ form.

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Step 4.1.1

Reorder terms.

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

Step 4.1.2

Remove parentheses.

$y = - \frac{3}{4} x$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 4 & - 3 \end{array}$

Step 5

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

Slope: $- \frac{3}{4}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 4 & - 3 \end{array}$

Step 6