Question

Gordon dreams of becoming the national spelling bee champion. He can already spell a lot of the words on his

study list, but he needs to learn even more. If Gordon studies for 2 hours, he will be able to spell a total of 300
words on the list. If he studies for 8 hours, he will be able to spell 400 words on the list.
In this relationship, x represents the time (in hours) that Gordon spends studying, and y represents the total
number of words on the study list that he can spell.
Graph two points for this relationship and the line passing through them.Is it proportional?

Answer 1

It is not a proportional relationship.

The graph of the two points have been attached.

Is it a proportional relationship?

x = the time (in hours) that Gordon spends studying

y = the total number of words on the study list that he can spell.

y = kx

Where,

k = constant of proportionality

Point 1:

(x, y) = (2, 300)

y = kx

300 = k × 2

300 = 2k

k = 300/2

k = 150

Point 2:

(x, y) = (8, 400)

y = kx

400 = k × 8

400 = 8k

k = 400/8

k = 50

Hence, the constant of proportionality is not equal, that is, it is not proportional.