The slope of the graph shown below is

B

Step-by-step explanation:

You can rule out answers A and C since the line is going down. Meaning that the answer has to be negative.

Next you have to find two points where the line intersects points on the graph. (one that I used (0,2) and (-4,7) ).

An easy way to do the math is finding the difference between the two x coordinates and y coordinates. (x,y) X are 0 and -4. Y are 2 and 7.

(x).  7-2=5

(y). 0-4= -4

In a fraction the layout is x over y. So it would be 5/-4. Rewritten is -5/4

-5/4

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is