Algebra Examples

$- \frac{2}{3} x + 2 y = - 7$

Step 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

Rewrite in slope-intercept form.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $x$ and $\frac{2}{3}$ .

$- \frac{x \cdot 2}{3} + 2 y = - 7$

Step 2.1.1.2

Move $2$ to the left of $x$ .

$- \frac{2 x}{3} + 2 y = - 7$

Step 2.2

Add $\frac{2 x}{3}$ to both sides of the equation.

$2 y = - 7 + \frac{2 x}{3}$

Step 2.3

Divide each term in $2 y = - 7 + \frac{2 x}{3}$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 y = - 7 + \frac{2 x}{3}$ by $2$ .

$\frac{2 y}{2} = \frac{- 7}{2} + \frac{\frac{2 x}{3}}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 7}{2} + \frac{\frac{2 x}{3}}{2}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{2} + \frac{\frac{2 x}{3}}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{7}{2} + \frac{\frac{2 x}{3}}{2}$

Step 2.3.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{7}{2} + \frac{2 x}{3} \cdot \frac{1}{2}$

Step 2.3.3.1.3

Cancel the common factor of $2$ .

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Step 2.3.3.1.3.1

Factor $2$ out of $2 x$ .

$y = - \frac{7}{2} + \frac{2 (x)}{3} \cdot \frac{1}{2}$

Step 2.3.3.1.3.2

Cancel the common factor.

$y = - \frac{7}{2} + \frac{2 x}{3} \cdot \frac{1}{2}$

Step 2.3.3.1.3.3

Rewrite the expression.

$y = - \frac{7}{2} + \frac{x}{3}$

Step 2.4

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

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Step 2.4.1

Reorder $- \frac{7}{2}$ and $\frac{x}{3}$ .

$y = \frac{x}{3} - \frac{7}{2}$

Step 2.4.2

Reorder terms.

$y = \frac{1}{3} x - \frac{7}{2}$