Question

writing systems of inequalities given graphsWrite a system of inequalities from each graph

Answer 1

EXPLANATION

The appropiate system of inequalities for the graph is:

(1) x=2 (There is a vertical line)

(2) y=mx + b where m is the slope and b is the y-intercept

The slope is given by the following relationship:

$\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}$

Where (x_1,y_1) and (x_2,y_2) are two ordered pairs from the line.

Considering either one ordered pair, as for instance, (x_1,y_1)=(0,-3) and (x_2,y_2)= (2,0) give us the appropiate slope.

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

Now, the line equation is as follows:

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

As the y-intercept is b=-3 the equation of the line is:

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

Hence, the system of equations is:

(1) x≥2

(2) y≤ (3/2)x - 3