Algebra Examples

$y < \frac{x^{2} - 5 x + 4}{x - 4}$

Step 1

Simplify $\frac{x^{2} - 5 x + 4}{x - 4}$ .

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Step 1.1

Factor $x^{2} - 5 x + 4$ using the AC method.

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Step 1.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $4$ and whose sum is $- 5$ .

$- 4, - 1$

Step 1.1.2

Write the factored form using these integers.

$y < \frac{(x - 4) (x - 1)}{x - 4}$

Step 1.2

Cancel the common factor of $x - 4$ .

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Step 1.2.1

Cancel the common factor.

$y < \frac{(x - 4) (x - 1)}{x - 4}$

Step 1.2.2

Divide $x - 1$ by $1$ .

$y < x - 1$

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 $y = m x + b$ , 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 $y = m x + b$ .

$m = 1$

$b = - 1$

Step 2.3

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

Slope: $1$

y-intercept: $(0, - 1)$

Slope: $1$

y-intercept: $(0, - 1)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $x - 1$ .

$y < x - 1$

Step 4