Algebra Examples

5 x - 2 y = 7

$5 x - 2 y = 7$

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 = 7 - 5 x

$- 2 y = 7 - 5 x$

Step 1.3

Divide each term in

- 2 y = 7 - 5 x

$- 2 y = 7 - 5 x$ by

- 2

$- 2$ and simplify.

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Step 1.3.1

Divide each term in

- 2 y = 7 - 5 x

$- 2 y = 7 - 5 x$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{7}{- 2} + \frac{- 5 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

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{7}{- 2} + \frac{- 5 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

Step 1.3.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{7}{- 2} + \frac{- 5 x}{- 2}

$y = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

y = \frac{7}{- 2} + \frac{- 5 x}{- 2}

$y = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

y = \frac{7}{- 2} + \frac{- 5 x}{- 2}

$y = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

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

Move the negative in front of the fraction.

y = - \frac{7}{2} + \frac{- 5 x}{- 2}

$y = - \frac{7}{2} + \frac{- 5 x}{- 2}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

y = - \frac{7}{2} + \frac{5 x}{2}

$y = - \frac{7}{2} + \frac{5 x}{2}$

y = - \frac{7}{2} + \frac{5 x}{2}

$y = - \frac{7}{2} + \frac{5 x}{2}$

y = - \frac{7}{2} + \frac{5 x}{2}

$y = - \frac{7}{2} + \frac{5 x}{2}$

y = - \frac{7}{2} + \frac{5 x}{2}

$y = - \frac{7}{2} + \frac{5 x}{2}$

Step 1.4

Write in

y = m x + b

$y = m x + b$ form.

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Step 1.4.1

Reorder

- \frac{7}{2}

$- \frac{7}{2}$ and

\frac{5 x}{2}

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

y = \frac{5 x}{2} - \frac{7}{2}

$y = \frac{5 x}{2} - \frac{7}{2}$

Step 1.4.2

Reorder terms.

y = \frac{5}{2} x - \frac{7}{2}

$y = \frac{5}{2} x - \frac{7}{2}$

y = \frac{5}{2} x - \frac{7}{2}

$y = \frac{5}{2} x - \frac{7}{2}$

y = \frac{5}{2} x - \frac{7}{2}

$y = \frac{5}{2} x - \frac{7}{2}$

Step 2

Using the slope-intercept form, the slope is

\frac{5}{2}

$\frac{5}{2}$ .

m = \frac{5}{2}

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

Step 3

The equation of a perpendicular line to

y = \frac{5}{2} x - \frac{7}{2}

$y = \frac{5}{2} x - \frac{7}{2}$ must have a slope that is the negative reciprocal of the original slope.

m_{perpendicular} = - \frac{1}{\frac{5}{2}}

$m_{perpendicular} = - \frac{1}{\frac{5}{2}}$

Step 4

Simplify the result.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

m_{perpendicular} = - (1 (\frac{2}{5}))

$m_{perpendicular} = - (1 (\frac{2}{5}))$

Step 4.2

Multiply

\frac{2}{5}

$\frac{2}{5}$ by

1

$1$ .

m_{perpendicular} = - \frac{2}{5}

$m_{perpendicular} = - \frac{2}{5}$

m_{perpendicular} = - \frac{2}{5}

$m_{perpendicular} = - \frac{2}{5}$

Step 5