Graph x/2+y/3>1

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

Step 1

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

Solve for $y$ .

Subtract $\frac{x}{2}$ from both sides of the inequality.

$\frac{y}{3} > 1 - \frac{x}{2}$

Multiply both sides by $3$ .

$\frac{y}{3} \cdot 3 > (1 - \frac{x}{2}) \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{y}{3} \cdot 3 > (1 - \frac{x}{2}) \cdot 3$

Rewrite the expression.

$y > (1 - \frac{x}{2}) \cdot 3$

Simplify the right side.

Simplify $(1 - \frac{x}{2}) \cdot 3$ .

Apply the distributive property.

$y > 1 \cdot 3 - \frac{x}{2} \cdot 3$

Multiply $3$ by $1$ .

$y > 3 - \frac{x}{2} \cdot 3$

Multiply $- \frac{x}{2} \cdot 3$ .

Multiply $3$ by $- 1$ .

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

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

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

Move the negative in front of the fraction.

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

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

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

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

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

$b = 3$

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

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

y-intercept: $(0, 3)$

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

y-intercept: $(0, 3)$

Step 3

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

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

Step 4

Graph x/2+y/3>1

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