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}=((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}=((0-(-3)))/((2-0))=(3)/(2)`

Now, the line equation is as follows:

`y=(3)/(2)x+b`

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

`y=(3)/(2)x-3`

Hence, the system of equations is:

(1) x≥2

(2) y≤ (3/2)x - 3