Question

“write an inequality to represent the graph.”

Answer 1

Answer:

The inequality for the given graph is $y>\frac{2}{3}x-1$.

Step-by-step explanation:

From the given graph it noticed that the line passing through (0,-1) and (3,1).

The equation of line passing through two points is defined as

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line is

$y+1=\frac{1+1}{3-0}(x-0)$

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

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

Therefore the related equation is $y=\frac{2}{3}x-1$.

The point (0,0) lies in the shaded region, therefore the point (0,0) is the solution of required inequality.

Put (0,0) in the related equation.

$0=\frac{2}{3}(0)-1$

$0=-1$

Since 0 is greater than -1, therefore the sign of inequality must be >. The related line is a dotted line, therefore we cannot use $\geq$.

Therefore the required inequality is

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