Question

The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function?

a. A 50-page photo album holds 400 photographs.
b. An 80-page photo album holds 560 photographs.
c. A 100-page photo album holds 8,000 photographs.
d. A 900-page photo album holds 8,400 photographs.

Answer 1

For a function to vary directly with x, means that its in this form: y = mx+b; you can solve this system of equation or simply look at the points and try to figure out how they relate. Then use that relation to pick an answer.

Answer 2

that didnt help

Answer 3

ok to break it down, we need to solve for the relationship between x and y correct? aka how does y change in respect to x.

Answer 4

the question says that they vary directly, which is basically saying that they vary in a y = ax + b form, where a and b are any real numbers.

Answer 5

so if we plug in the two points we have into the above equation we can solve of a and b.

24 = a*3 + b // 56 = a*7 + b

if 24 = a*3 + b, that means that b = 24 - a*3, we can now substitute b in the other equation to get:

56 = a*7 + 24 - a*3

simplify this down we get:
56 - 24 = a*4
32 = a*4
a = 8;

put back a into any of the previous equations and we can solve for b
24 = 8*3 + b
b = 0;

Now we have our equation/relation:
y = 8x; we could have also looked at the points and realized that y is 8 times x.

Now we can look at the answer choices and find which follows the same rule.

Answer 6

So A ?

Answer 7

yep