Algebra Examples

$y + 4 x \leq x^{2} + 2$

Step 1

Subtract $4 x$ from both sides of the inequality.

$y \leq x^{2} + 2 - 4 x$

Step 2

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

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

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 2.1.2

Move $2$ .

$y \leq x^{2} - 4 x + 2$

Step 2.2

The equation is not linear, so a constant slope does not exist.

Not Linear

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x^{2} + 2 - 4 x$ .

$y \leq x^{2} + 2 - 4 x$

Step 4