Algebra Examples

$2 x + 3 y < 6$

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

Subtract $2 x$ from both sides of the inequality.

$3 y < 6 - 2 x$

Step 1.1.2

Divide each term in $3 y < 6 - 2 x$ by $3$ and simplify.

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Step 1.1.2.1

Divide each term in $3 y < 6 - 2 x$ by $3$ .

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

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $3$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $6$ by $3$ .

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

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

$y < 2 - \frac{2 x}{3}$

Step 1.2

Rearrange terms.

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

Step 1.3

Reorder terms.

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

Step 1.4

Remove parentheses.

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

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

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

Step 4