Pre-Algebra Examples

$3 x - 2 y = 7 x - 5$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Subtract $3 x$ from both sides of the equation.

$- 2 y = 7 x - 5 - 3 x$

Step 1.2.2

Subtract $3 x$ from $7 x$ .

$- 2 y = 4 x - 5$

Step 1.3

Divide each term in $- 2 y = 4 x - 5$ by $- 2$ and simplify.

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Step 1.3.1

Divide each term in $- 2 y = 4 x - 5$ by $- 2$ .

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

Step 1.3.2

Simplify the left 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

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $y$ by $1$ .

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Cancel the common factor of $4$ and $- 2$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $4 x$ .

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

Step 1.3.3.1.1.2

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y = - 1 \cdot (2 x) + \frac{- 5}{- 2}$

Step 1.3.3.1.2

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

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

Step 1.3.3.1.3

Multiply $2$ by $- 1$ .

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

Step 1.3.3.1.4

Dividing two negative values results in a positive value.

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

Step 2

Using the slope-intercept form, the slope is $- 2$ .

$m = - 2$

Step 3