Algebra Examples

x - y > 0

$x - y > 0$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

x

$x$ from both sides of the inequality.

- y > - x

$- y > - x$

Step 1.2

Divide each term in

- y > - x

$- y > - x$ by

- 1

$- 1$ and simplify.

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Step 1.2.1

Divide each term in

- y > - x

$- y > - x$ by

- 1

$- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

\frac{- y}{- 1} < \frac{- x}{- 1}

$\frac{- y}{- 1} < \frac{- x}{- 1}$

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{- x}{- 1}

$\frac{y}{1} < \frac{- x}{- 1}$

Step 1.2.2.2

Divide

y

$y$ by

1

$1$ .

y < \frac{- x}{- 1}

$y < \frac{- x}{- 1}$

y < \frac{- x}{- 1}

$y < \frac{- x}{- 1}$

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{x}{1}

$y < \frac{x}{1}$

Step 1.2.3.2

Divide

x

$x$ by

1

$1$ .

y < x

$y < x$

y < x

$y < x$

y < x

$y < x$

y < x

$y < x$

Step 2

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

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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

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 = 0

$b = 0$

Step 2.3

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, 0)

$(0, 0)$

Slope:

1

$1$

y-intercept:

(0, 0)

$(0, 0)$

Step 3

Graph a dashed line, then shade the area below the boundary line since

y

$y$ is less than

x

$x$ .

y < x

$y < x$

Step 4