Algebra Examples

$5 x - y < 5$

Step 1

Write in $y = m x + b$ form.

Tap for more steps...

Step 1.1

Solve for $y$ .

Tap for more steps...

Step 1.1.1

Subtract $5 x$ from both sides of the inequality.

$- y < 5 - 5 x$

Step 1.1.2

Divide each term in $- y < 5 - 5 x$ by $- 1$ and simplify.

Tap for more steps...

Step 1.1.2.1

Divide each term in $- y < 5 - 5 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{5}{- 1} + \frac{- 5 x}{- 1}$

Step 1.1.2.2

Simplify the left side.

Tap for more steps...

Step 1.1.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{5}{- 1} + \frac{- 5 x}{- 1}$

Step 1.1.2.2.2

Divide $y$ by $1$ .

$y > \frac{5}{- 1} + \frac{- 5 x}{- 1}$

Step 1.1.2.3

Simplify the right side.

Tap for more steps...

Step 1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.1.2.3.1.1

Divide $5$ by $- 1$ .

$y > - 5 + \frac{- 5 x}{- 1}$

Step 1.1.2.3.1.2

Move the negative one from the denominator of $\frac{- 5 x}{- 1}$ .

$y > - 5 - 1 \cdot (- 5 x)$

Step 1.1.2.3.1.3

Rewrite $- 1 \cdot (- 5 x)$ as $- (- 5 x)$ .

$y > - 5 - (- 5 x)$

Step 1.1.2.3.1.4

Multiply $- 5$ by $- 1$ .

$y > - 5 + 5 x$

Step 1.2

Rearrange terms.

$y > 5 x - 5$

Step 2

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

Tap for more steps...

Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 5$

$b = - 5$

Step 2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $5$

y-intercept: $(0, - 5)$

Slope: $5$

y-intercept: $(0, - 5)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $5 x - 5$ .

$y > 5 x - 5$

Step 4