Tip #11 to Get a Top SAT Math Score

Slope questions appear on every SAT. This topic could fill a college–level course, but the SAT tests only a few concepts.

Most importantly, to find the slope of two ordered pairs, use the slope formula:

You should also know these other groovy SAT slope facts:

• The slope of a line measures its steepness—the steeper the line, the bigger the slope.
• A line has a positive slope if it rises from left to right.
• A line has a negative slope if it falls from left to right.
• A horizontal line has a slope of 0.

Let's look at this question:

Solution: Plug the two points into the slope equation.

Once you have , you can simply "Use the Answers" and try each answer choice to see which one makes the equation work. Skill Preview: As we will see in Skill 20, you could also cross–multiply to solve this equation.

Correct answer: E

Example Problems

Easy

1. If the slope of a line through the points (3, a) and (–2, –4) is , what is the value of a ?
   1. A –2
   2. B –1
   3. C 0
   4. D 1
   5. E 2
2. What is the slope of the line through the point (2, –3) and the origin?
   1. A –2.5
   2. B –1.5
   3. C –1
   4. D 0.5
   5. E 2.5
3. Which of the following is closest to the slope of the line in the figure below?

Medium

4. In the figure below, the line containing (a, b) passes through the origin. What is the value of ?



1. A –1
2. B 0
3. C 1
4. D 3
5. E Undefined

Hard

5. In the xy coordinate plane below, the indicated diameters of the two circles shown are parallel to the y axis. If the points M and N are centers of the circles, what is the slope of line MN (not shown)?

Answers

1. B   Plug the two points into the slope equation.



Once you have , you can simply "Use the Answers" and try each answer choice to see which one makes the equation work. You could also cross–multiply (see Skill 20).

2. B   This question is exactly like Question 1. You are given 2 points, and you simply plug them into the slope formula. The only twist is that the question refers to the origin as one of the two points so you have to know that "origin" means (0, 0), which is just vocab. Know it (which you do now) and you get it correct!



Notice how is not a choice. Don't be thrown. Be confident, unshakeable! After you finish this book, you will always know what to do; don't let the question intimidate you. So, which choice matches our ? Just enter it in your calculator, remember that means "–3 divided by 2," and you get – 1.5. Bingo!

3. C   Use two points to count the , the change in y over the change in x.
4. C   Remember that pictures on the SAT are drawn exactly to scale (we'll talk more about this excellent strategy in Skill 21). So just use the picture to determine the values of (a, b); it looks like (4, 4). The question just asks for , so the answer is choice C, since = 1.
5. B To get the slope of MN, we must know the coordinates for M and for N. Since these points are centers of the circles, they are halfway between the endpoints of each diameter shown. So M equals (2, 1) and N equals (7, 3). Now we plug these into the slope formula.

Go to: Tip #12