Which of the following answer choices are correct ?

Okay, here we go. 

So, given the formula, we can just plug in the numbers on the number lines. So for example:

On the first graph, it starts at 4 and goes to 5. Let's plug those in:
-6(4)+42<24
-24+42<24
18<24
18 is less than 24, so this is true so far.

moving on:
-6(5)+42<24
-30+42<24
12<24
true, again. The first graph seems correct. Let's check our answers by using the third graph where the numbers 3,2, and 1 are checked.

-6(3)+42<24
-18+42<24
24<24
24 is equal to 24, not less than, so the third graph is wrong. 

Knowing this, we can use the process of elimination. We know 4 and 5 fit the equation and 3, 2, and 1 don't. This means that the graph with 4 and 5 marked is the correct one aka the first graph

Hopefully this is correct and I helped at all :)

If you need an equation, it would be y=2x+8, y would be how long it grew, x being weeks.if you need how long he was asleep, it would be 4 weeks if he started with no beard, the equation would be x=8÷2if he did have a beard before hand, the equation would be 2w+x=8