Graph 3/2y-2x>=1

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

Step 1

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

Solve for $y$ .

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

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

Add $2 x$ to both sides of the inequality.

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

Multiply both sides by $2$ .

$\frac{3 y}{2} \cdot 2 \geq (1 + 2 x) \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 y}{2} \cdot 2 \geq (1 + 2 x) \cdot 2$

Rewrite the expression.

$3 y \geq (1 + 2 x) \cdot 2$

Simplify the right side.

Simplify $(1 + 2 x) \cdot 2$ .

Apply the distributive property.

$3 y \geq 1 \cdot 2 + 2 x \cdot 2$

Simplify the expression.

Multiply $2$ by $1$ .

$3 y \geq 2 + 2 x \cdot 2$

Multiply $2$ by $2$ .

$3 y \geq 2 + 4 x$

Reorder $2$ and $4 x$ .

$3 y \geq 4 x + 2$

Divide each term in $3 y \geq 4 x + 2$ by $3$ and simplify.

Divide each term in $3 y \geq 4 x + 2$ by $3$ .

$\frac{3 y}{3} \geq \frac{4 x}{3} + \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \geq \frac{4 x}{3} + \frac{2}{3}$

Divide $y$ by $1$ .

$y \geq \frac{4 x}{3} + \frac{2}{3}$

Reorder terms.

$y \geq \frac{4}{3} x + \frac{2}{3}$

Step 2

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

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

$m = \frac{4}{3}$

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

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

Slope: $\frac{4}{3}$

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

Slope: $\frac{4}{3}$

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

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{4}{3} x + \frac{2}{3}$ .

$y \geq \frac{4}{3} x + \frac{2}{3}$

Step 4

Graph 3/2y-2x>=1

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