Algebra Examples

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

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $- \frac{2 y}{3} = 2 x$ .

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

Step 1.2

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

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

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

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

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Step 1.3.1.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 1.3.1.1.1.2

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

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

Step 1.3.1.1.1.3

Factor $3$ out of $- 3$ .

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

Step 1.3.1.1.1.4

Cancel the common factor.

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

Step 1.3.1.1.1.5

Rewrite the expression.

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

Step 1.3.1.1.2

Cancel the common factor of $2$ .

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Step 1.3.1.1.2.1

Factor $2$ out of $- 2 y$ .

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

Step 1.3.1.1.2.2

Cancel the common factor.

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

Step 1.3.1.1.2.3

Rewrite the expression.

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

Step 1.3.1.1.3

Multiply.

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Step 1.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.3.1.1.3.2

Multiply $y$ by $1$ .

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

Step 1.3.2

Simplify the right 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

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 1.3.2.1.2

Factor $2$ out of $2 x$ .

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

Step 1.3.2.1.3

Cancel the common factor.

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

Step 1.3.2.1.4

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