Select the inequality that corresponds to the figure:
a.2x + y < 7
b. 2x - y < 7
c. 2x - y > -7
d. none of the above.

C. 2x-y>-7

Step-by-step explanation:

The Line is not part of the region since is drawn in the graph using a dotted line, but we still need to find its equation.

The equation of a line is y=mx+b, where 'm' is the slope.

'm' can be obtained using the following formula.

To find the slope, as well 'b' we need points from the line, those will be (-6,-5), (0,7) as (x2,y2) and (x1,y1) respectively

Evaluating those point in the formula we have 'm' =2

Using now the above result and the point (0,7) in the equation y=mx+b, we obtain the value for 'b'.

7=2*0+b7

b=7

Hence our line is y=2x+7, and if we write it in standard form we obtain the following> y-2x=7.

Now, since our line is not part of the region, and the region is below that line, there is the < sign.

Hence the inequality that corresponds to the figure is y-2x<7 or, if we multiply by -1 (changin orientation of signs)   2x-y>-7

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.

x:       y:  

-1         4

0         4

1         6

2         18

3         20