help! I really need this answer and im totally stuck!

Question

The amount Byron earns is directly proportional to the number of hours he works. If Byron earns $60.80 for 4 hours of work, find the constant of proportionality, and write a direct proportion equation. (k=y/x)

Answer 1

If Byron earns $k for every 1 hour of work,

for 4 hours of work, he will earn 4*k.

Therefore, in this problem, x is the number of hours and y is the total earnings in dollars.

Total earnings y is obtained by multiplying the number of hours x by earnings per hour k.

Now, Direct proportion equation will be y = kx.

Given: Byron earns $60.80 for 4 hours of work.

=> 60.80 = k*4

=> k = 60.80/4 = 15.2

Therefore, direct proportion equation for this problem is obtained by substituting the value of k in y = kx.

=> y = 15.2x

(From this equation we can find the total earnings y for any given number of hours x. Or, for a given total earnings, the number of hours can be calculated.)

Answer 2

When direct proportional is mentioned in a problem, it always means:

y = kx

where k is the constant of proportionality. Given an x and a y, all you have to do is compute k. The problem already gave the hint, k = y/x.

For this problem, x = 4 and y = 60.80, so k = 60.80/4 = 15.2.

Therefore, the direct proportion for this case is:

y = 15.2x

Note: Sometimes you will see a direct proportional equation written as:

y ∝ x and is read as y is directly proportional to x,

which means the same as y = kx