Graph y>=((-2x+3)(x-2))/(x-2)

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

Find the slope and the y-intercept for the boundary line.

Rewrite in slope-intercept form.

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

$y = m x + b$

Simplify the right side.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Divide $- 2 x + 3$ by $1$ .

$y \geq - 2 x + 3$

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

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

$m = - 2$

$b = 3$

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

Slope: $- 2$

y-intercept: $(0, 3)$

Slope: $- 2$

y-intercept: $(0, 3)$

Slope: $- 2$

y-intercept: $(0, 3)$

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

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