Graph 2x+2y>=3

$2 x + 2 y \geq 3$

Step 1

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

Solve for $y$ .

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

$2 y \geq 3 - 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- x$ by $1$ .

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

Rearrange terms.

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

Step 2

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = - 1$

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

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

Slope: $- 1$

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

Slope: $- 1$

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

Step 3

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

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

Step 4

Graph 2x+2y>=3

Related Questions

Support LCMGCF.com by disabling your adblocker.