Algebra Examples

$y < \frac{(x + 3) (x - 4)}{x - 4}$

Step 1

Find the slope and the y-intercept for the boundary line.

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Step 1.1

Rewrite in slope-intercept form.

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Step 1.1.1

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 1.1.2

Simplify the right side.

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Step 1.1.2.1

Cancel the common factor of $x - 4$ .

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Step 1.1.2.1.1

Cancel the common factor.

$y < \frac{(x + 3) (x - 4)}{x - 4}$

Step 1.1.2.1.2

Divide $x + 3$ by $1$ .

$y < x + 3$

Step 1.2

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

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Step 1.2.1

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

$m = 1$

$b = 3$

Step 1.2.2

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

Slope: $1$

y-intercept: $(0, 3)$

Slope: $1$

y-intercept: $(0, 3)$

Slope: $1$

y-intercept: $(0, 3)$

Step 2

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{(x + 3) (x - 4)}{x - 4}$ .

$y < \frac{(x + 3) (x - 4)}{x - 4}$

Step 3