Algebra Examples

$y \leq 3 + \frac{1}{2} x$

Step 1

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

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Step 1.1

Simplify $3 + \frac{1}{2} x$ .

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Step 1.1.1

Combine $\frac{1}{2}$ and $x$ .

$y \leq 3 + \frac{x}{2}$

Step 1.1.2

Reorder $3$ and $\frac{x}{2}$ .

$y \leq \frac{x}{2} + 3$

Step 1.2

Reorder terms.

$y \leq \frac{1}{2} x + 3$

Step 2

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

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Step 2.1

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

$m = \frac{1}{2}$

$b = 3$

Step 2.2

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 3)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 3)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x + 3$ .

$y \leq \frac{1}{2} x + 3$

Step 4