Graph y>=4xy

$y \geq 4 x y$

Step 1

Solve for $y$ .

Subtract $4 x y$ from both sides of the inequality.

$y - 4 x y \geq 0$

Factor $y$ out of $y - 4 x y$ .

Factor $y$ out of $y^{1}$ .

$y \cdot 1 - 4 x y \geq 0$

Factor $y$ out of $- 4 x y$ .

$y \cdot 1 + y (- 4 x) \geq 0$

Factor $y$ out of $y \cdot 1 + y (- 4 x)$ .

$y (1 - 4 x) \geq 0$

Divide each term in $y (1 - 4 x) \geq 0$ by $1 - 4 x$ and simplify.

Divide each term in $y (1 - 4 x) \geq 0$ by $1 - 4 x$ .

$\frac{y (1 - 4 x)}{1 - 4 x} \geq \frac{0}{1 - 4 x}$

Simplify the left side.

Cancel the common factor of $1 - 4 x$ .

Cancel the common factor.

$\frac{y (1 - 4 x)}{1 - 4 x} \geq \frac{0}{1 - 4 x}$

Divide $y$ by $1$ .

$y \geq \frac{0}{1 - 4 x}$

Simplify the right side.

Divide $0$ by $1 - 4 x$ .

$y \geq 0$

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 $y = m x + b$ .

$m = 0$

$b = 0$

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

Slope: $0$

y-intercept: $(0, 0)$

Slope: $0$

y-intercept: $(0, 0)$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $0$ .

$y \geq 0$

Step 4