Question

MEDAL AND FAN

Which of the following inequalities is graphed above?

-9x - y > -5

-9x + y < -5

-9x - y < -5

9x + y < 5

Answer 1

@ybarrap

Answer 2

B

Answer 3

So we need the equation of the line that partitions the gray area from the white.

The partition is separated by a line that can be represented by
y=mx+b

where m is the slope and b is the y-intercept

Let's find two points on the line.

I see that at x=0 y = 5 and at x=1 y=-4

So the 1st point gives is our y-intercept, this is where the line intercepts the y-axis and this happens when x=0.

The slope is
$$
m=\cfrac{-4-5}{1-0}=\cfrac{-9}{1}=-9
$$

Therefore, the line that divides both areas is y=-9x+5.

We then can describe the gray area by all points greater than this number:
$$
y\gt-9x+5\\
-5\gt-9x-y\\
-9x-y \lt -5
$$

Does this make sense?