Question 828298
AS A MATH CLASS PROBLEM:
If this is a problem for a math class in school, you are probably expected to do it a certain way, following a certain procedure, and/or using a certain formula, rather than using your brain. That kind of "educational malpractice" causes many brains to atrophy, and convinces many people that doing well in math (and physics) is just a question of memorizing a lot of facts and formulas. So wrong, so sad!
 
You are probably expected to think of this as an "inverse' relation, as in
"for a certain fixed distance, the number of gallons of fuel consumed is inversely proportional to the mileage (miles per gallon) of the vehicle"
The more economic your vehicle (yielding more miles per gallon of fuel), the less fuel you will need to go from home to work, or from home to school.
If you use a small car that gives you twice as many miles per gallon as your neighbors big pick up truck, you will use half the amount of fuel your neighbor uses.
You probably were given the formula {{{y=k/x}}} for when {{{y}}} is inversely proportional to {{{x}}} .
You were probably told that {{{k}}} is a constant,
and that if you know one (x,y) pair in that relationship, you can find all the others.
Take, for example,
Mileage (miles per gallon), x = 15 Gas (gallons) y =5.5
Substituting those values into {{{y=k/x}}}
we find {{{5.5=k/5}}} as an equation to solve for {{{k}}} .
{{{k/15=5.5}}} --> {{{k=5.5*15}}} --> {{{highlight(k=82.5)}}}
Now you have a relation (and more specifically, a function) to calculate {{{y}}} for any {{{x}}} :
{{{y=82.5/x}}}
So, for {{{x=33}}},
{{{y=82.5/33}}} --> {{{highlight(y=2.5)}}}
Indeed, you can build the whole table with that "formula", which makes me wonder why they gave you so many lines in that table.
 
AS AN SAT PROBLEM:
In this case, you are expected to use your brain, and forget formulas.
Think as a fifth grader should be able to think.
If the guy with the inefficient boat doing just x=16.5 miles per gallon needs y=5 gallons to go a certain distance,
your twice as efficient boat, doing twice as many miles per gallons (x=33), will need half as much fuel:
{{{y=5gal/2=highlight(2.5gal)}}}.
 
IF YOU HAD JUST A TABLE of x and y values (maybe data collected from a science lab experiment), you would want to plot your data, and would get
{{{drawing(300,300,-10,40,-2,8,
grid(1),
red(circle(11,7.5,1)),red(circle(13.75,6,1)),
red(circle(15,5.5,1)),red(circle(16.5,5,1)),
red(circle(27.5,3,1))
)}}} Excel, or any statistical software package would let you make that graph and calculate best fit curves for several models (theories on whether y varies linearly with x, or with x squared, or it is an exponential function, or some other relation). It will tell you that the linear model does not fit very well,
but you can see that the points do not fit a straight line. They suggest a curve. If the statistic program had an inversely proportional model, it would tell you that it fits the data perfectly.
Otherwise, if you were in calculus, or pre-calculus class you might say the plotted points make the relation look like a hyperbola, with the x- and y-axes as aymptotes.
So you would try to plot {{{y}}} against {{{1/x}}}. Then you would find an absolutely perfect linear fit, and would realize that real data cannot be that perfect. Your lab partner must have fabricated the data.