Algebra Examples

$y + 2 \leq - \frac{2}{3} x + 4$

Step 1

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

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

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

$y + 2 \leq - \frac{x \cdot 2}{3} + 4$

Step 1.1.1.2

Move $2$ to the left of $x$ .

$y + 2 \leq - \frac{2 x}{3} + 4$

Step 1.1.2

Move all terms not containing $y$ to the right side of the inequality.

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Step 1.1.2.1

Subtract $2$ from both sides of the inequality.

$y \leq - \frac{2 x}{3} + 4 - 2$

Step 1.1.2.2

Subtract $2$ from $4$ .

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

Step 1.2

Reorder terms.

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

Step 1.3

Remove parentheses.

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

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 $y = m x + b$ .

$m = - \frac{2}{3}$

$b = 2$

Step 2.2

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, 2)$

Slope: $- \frac{2}{3}$

y-intercept: $(0, 2)$

Step 3

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

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

Step 4