Pre-Algebra Examples

5 x - 2 y

$5 x - 2 y$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

5 x

$5 x$ from both sides of the equation.

- 2 y = - 5 x

$- 2 y = - 5 x$

Step 1.2

Divide each term in

- 2 y = - 5 x

$- 2 y = - 5 x$ by

- 2

$- 2$ and simplify.

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Step 1.2.1

Divide each term in

- 2 y = - 5 x

$- 2 y = - 5 x$ by

- 2

$- 2$ .

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

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

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

Step 1.2.2.1.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Dividing two negative values results in a positive value.

y = \frac{5 x}{2}

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

y = \frac{5 x}{2}

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

y = \frac{5 x}{2}

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

y = \frac{5 x}{2}

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

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Reorder terms.

y = \frac{5}{2} x

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

y = \frac{5}{2} x

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

Step 3

Use the slope-intercept form to find the slope and y-intercept.

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Step 3.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = \frac{5}{2}

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

b = 0

$b = 0$

Step 3.2

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

\frac{5}{2}

$\frac{5}{2}$

y-intercept:

(0, 0)

$(0, 0)$

Slope:

\frac{5}{2}

$\frac{5}{2}$

y-intercept:

(0, 0)

$(0, 0)$

Step 4

Any line can be graphed using two points. Select two

x

$x$ values, and plug them into the equation to find the corresponding

y

$y$ values.

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Step 4.1

Reorder terms.

y = \frac{5}{2} x

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

Step 4.2

Create a table of the

x

$x$ and

y

$y$ values.

\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 5 \end{array}

$\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 5 \end{array}$

\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 5 \end{array}

$\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 5 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope:

\frac{5}{2}

$\frac{5}{2}$

y-intercept:

(0, 0)

$(0, 0)$

\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 5 \end{array}

$\begin{array}{c} x & y \\ 0 & 0 \\ 2 & 5 \end{array}$

Step 6