Answer:
Option D is correct
Step-by-step explanation:
For this question we would need the equation of line since this is a multiple choice question you wouldn't have enough time to find out the equation so we need to be FAST
If we see all the four options at first glance option C or option D seem correct because the line represents a rise in values of x and y respectively, which means x increases with respect to y. So the slope/gradient in other words m should be positive so option A and B are ruled out because the equation of line is written as
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept so seeing the graph our equation of line should be
[tex]y=mx-2[/tex]
where b = -2 because value of b corresponds to y-intercept which means the where the graph intersects the y-axis in this case its -2
where m is positive in this case 5 thus
[tex]y=5x-2[/tex]
if we try to rearrange the four choices option C and D give us the above equation and option A and B give us
[tex]y=-5x+2[/tex]
which is wrong !
Now, regarding the inequality sign the graph represents
[tex]y=5x-2[/tex]
and the area which is shaded in blue is the region lower the line which means it should be
[tex]y\leq 5x-2[/tex]
in this case its D if we rearrange it
I have two images so you understand it better visually
As you can see in both forms are shaded region is the same so option D is correct
