Algebra Examples

5 x - 2 y = 10

$5 x - 2 y = 10$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Subtract

5 x

$5 x$ from both sides of the equation.

- 2 y = 10 - 5 x

$- 2 y = 10 - 5 x$

Step 1.3

Divide each term in

- 2 y = 10 - 5 x

$- 2 y = 10 - 5 x$ by

- 2

$- 2$ and simplify.

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Step 1.3.1

Divide each term in

- 2 y = 10 - 5 x

$- 2 y = 10 - 5 x$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 5 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 5 x}{- 2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 5 x}{- 2}$

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{10}{- 2} + \frac{- 5 x}{- 2}$

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

Divide

$10$ by

$- 2$ .

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

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.4

Write in

$y = m x + b$ form.

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Step 1.4.1

Reorder

$- 5$ and

$\frac{5 x}{2}$ .

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

Step 1.4.2

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is

$\frac{5}{2}$ .

$m = \frac{5}{2}$

Step 3

All lines that are parallel to

$y = \frac{5}{2} x - 5$ have the same slope of

$\frac{5}{2}$ .

$m_{parallel} = \frac{5}{2}$

Step 4