Algebra Examples

$y \leq - \frac{5}{6} x + \frac{2}{3}$

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

Simplify each term.

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Step 1.1.2.1.1

Combine $x$ and $\frac{5}{6}$ .

$y \leq - \frac{x \cdot 5}{6} + \frac{2}{3}$

Step 1.1.2.1.2

Move $5$ to the left of $x$ .

$y \leq - \frac{5 x}{6} + \frac{2}{3}$

Step 1.1.3

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

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Step 1.1.3.1

Reorder terms.

$y \leq - (\frac{5}{6} x) + \frac{2}{3}$

Step 1.1.3.2

Remove parentheses.

$y \leq - \frac{5}{6} x + \frac{2}{3}$

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 $y = m x + b$ .

$m = - \frac{5}{6}$

$b = \frac{2}{3}$

Step 1.2.2

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

Slope: $- \frac{5}{6}$

y-intercept: $(0, \frac{2}{3})$

Slope: $- \frac{5}{6}$

y-intercept: $(0, \frac{2}{3})$

Slope: $- \frac{5}{6}$

y-intercept: $(0, \frac{2}{3})$

Step 2

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{5}{6} x + \frac{2}{3}$ .

$y \leq - \frac{5}{6} x + \frac{2}{3}$

Step 3