The key to these quantitative comparison problems is to figure out the worth of both quantities, or figure out whether evaluating the quantities is even possible.  In this case, evaluating the quantities is a fairly straightforward case of figuring out the intercepts of two different lines, which is possible.  Therefore, you can already discount "the relationship cannot be determined from the information given".

To solve quantity A:  is in  form, where  is the -intercept. Therefore, the -intercept is equal to . 

To solve quantity B: , you have to sole for the  intercept.  The quickest way to figure out the answer is to remember that the  axis exists at the line , therefore to find out where the line crosses the  axis, you can set  and solve for .  

-3.5 = .5x - 1.5

Both quantity A and quantity B , therefore the two quantities are equal.

To find the -intercept, you must plug  in for .  

This leaves you with 

.  

Then you must get you by itself so you add  to both sides 

.  

Then divide both sides by  to get 

.  

For the coordinate point,  goes first then  and the answer is .

Solve for  so that the equation resembles the  form. This equation becomes . In this form, the  is the slope, which is .

To find the -intercept, you need to find the value of the equation where .  The easiest way to do this is to substitute in  for your value of  and see where you get  for .  If you do this for each of your equations proposed as potential answers, you find that  is the answer.

Substitute in  for :

If  has a -intercept of , then it must pass through the point .

If its -intercept is , then it must through the point .

The slope of this line is .

Therefore, any line perpendicular to this line must have a slope equal to the negative reciprocal, which is . Only  has a slope of .

The base of the original cylinder would have been πr², and the outer face would have been 2πrh, where h is the height of the cylinder.

Let's represent the original area with A, the original radius with r, and the new radius with R: therefore, we know πR² = 4A, or πR² = 4πr². Solving for R, we get R = 2r; therefore, the new outer face of the cylinder will have an area of 2πRh or 2π2rh or 4πrh, which is double the original face area; thus the percentage of increase is 100%. (Don't be tricked into thinking it is 200%. That is not the percentage of increase.)

We need the formula for the surface area of a cylinder: SA = 2πr² + 2πrh. This formula has π in it, but the answer choices don't. This means we must approximate π. None of the answers are too close to each other so we could really even use 3 here, but it is safest to use 3.14 as an approximate value of π.

Then SA = 2 * 3.14 * 17² + 2 * 3.14 * 17 * 3 ≈ 2137

surface area of a cylinder

= 2πr² + 2πrh

= 2π * 6² + 2π * 6 *9

= 180π

There is no need to do the actual computations here to find the two volumes. The volume of a cone is exactly 1/3 the volume of a cylinder with the same height and radius. That means the two quantities are equal. The formulas show this relationship as well: volume of a cone = πr²h/3 and volume of a cylinder = πr²h. 

The volume of any solid figure is . In this case, the volume of the cylinder is  and its height is , which means that the area of its base must be . Working backwards, you can figure out that the radius of a circle of area  is . The circumference of a circle with a radius of  is , which is greater than .