Algebra Examples

x - y = 3

$x - y = 3$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

x

$x$ from both sides of the equation.

- y = 3 - x

$- y = 3 - x$

Step 1.2

Divide each term in

- y = 3 - x

$- y = 3 - x$ by

- 1

$- 1$ and simplify.

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Step 1.2.1

Divide each term in

- y = 3 - x

$- y = 3 - x$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{3}{- 1} + \frac{- x}{- 1}

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} = \frac{3}{- 1} + \frac{- x}{- 1}

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

Step 1.2.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{3}{- 1} + \frac{- x}{- 1}

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

y = \frac{3}{- 1} + \frac{- x}{- 1}

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide

3

$3$ by

- 1

$- 1$ .

y = - 3 + \frac{- x}{- 1}

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

y = - 3 + \frac{x}{1}

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

Step 1.2.3.1.3

Divide

x

$x$ by

1

$1$ .

y = - 3 + x

$y = - 3 + x$

y = - 3 + x

$y = - 3 + x$

y = - 3 + x

$y = - 3 + x$

y = - 3 + x

$y = - 3 + x$

y = - 3 + x

$y = - 3 + x$

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

- 3

$- 3$ and

x

$x$ .

y = x - 3

$y = x - 3$

y = x - 3

$y = x - 3$

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 = 1

$m = 1$

b = - 3

$b = - 3$

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:

1

$1$

y-intercept:

(0, - 3)

$(0, - 3)$

Slope:

1

$1$

y-intercept:

(0, - 3)

$(0, - 3)$

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

- 3

$- 3$ and

x

$x$ .

y = x - 3

$y = x - 3$

Step 4.2

Create a table of the

x

$x$ and

y

$y$ values.

\begin{matrix} x & y 0 & - 3 1 & - 2 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 3 \\ 1 & - 2 \end{array}$

\begin{matrix} x & y 0 & - 3 1 & - 2 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 3 \\ 1 & - 2 \end{array}$

Step 5

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

Slope:

$1$

y-intercept:

$(0, - 3)$

$\begin{array}{c} x & y \\ 0 & - 3 \\ 1 & - 2 \end{array}$

Step 6