# Equation of a Line

How do you make sure that you have the best doctors and the best conditions for patients?  First there was a push for doctors to get more sleep.  Now there is a push to make sure that doctors are getting more hours to finish their work.  Take a look at the debate in this current event.  Write down the broad themes in this article, and the specific details that will make you sound informed.  Then try linking this current event to the following previous SAT essay prompts:  Is there always another explanation or another point of view?  Can success be disastrous?  Should people let their feelings guide them when they make important decisions?  Should people change their decisions when circumstances change, or is it best for them to stick with their original decisions?

## Geometry: Coordinate Geometry

Read the following SAT test question and then select the correct answer.

Always read the question carefully and identify the bottom line.  Assess your options for reaching the bottom line, and use the most efficient method to attack the problem.  When you have an answer, loop back to verify that your answer matches the bottom line.

If the graph of the function f is a line with slope 2, which of the following could be the equation of f?

Bottom Line: WOTF (which of the following)

Assess your Options:  For a “which of the following” question you should look at the answers choices, but not until you have used what you know about the equation of a line to decide what kind of equation you need to find.  Start with the information that you are given.

Attack the Problem:  Remember the generic equation for a line is y = mx + b.  In any equation, f(x) and y can mean the same thing.  The variable m is the slope of the line.  You know that your slope must be 2.  Plug that 2 into the equation.  You now have:

f(x) = 2x + b

(The variable b is the y-intercept.  You were not told anything about the y-intercept, so that could be any number.  All you need to do is match the part that you do know, the 2x.)

Loop Back:  You used all the information that you were given, so look down at your answer choices.

(A) f(x) = 4x - 2
(B) f(x) = 2x + 4
(C) f(x) = -2x – 2
(D) $f(x)=\frac{1}{2}x+2$
(E) $f(x)=-\frac{1}{2}x+\frac{1}{2}$

On sat.collegeboard.org, 64% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

# Equation of a Line

Almost any student who has studied triangles has heard of Pythagoras (the author of the Pythagorean Theorem). He lived from roughly 569 B.C. to 500 B.C. and is considered by many to have been the first pure mathematician. In addition to mathematics, Pythagoras also studied music and religion. He is a fascinating historical figure and would make a great "Excellent Example" for your essay. You can lean more about Pythagoras here

## 6/26 Equation of a line

Read the following SAT test question and then select the correct answer choice.

As always, remember to follow the Knowsys method for math. Read the problem carefully and identify the bottom line (what you are looking for). Then, consider your options. How could you solve it? How should you solve it? Next, attack the problem using the method that you selected. Finally, loop back and verify that your answer matches the bottom line. Do not forget the last step. If the problems asks for what "must be false" and you choose an answer that "could be true" you will lose points (even if you solved the equation correctly).

If the graph of the function f is a line with a slope of 2, which of the following could be the equation of f?

Whenever a problem seems straightforward and simple (as this one does), make sure that you read it carefully. Also, look at where in the section the problem appears. If it is one of the last problems in the section, it's probably a hard problem (so if it looks easy, you probably have fallen for a trap). In this case, this problem really is as easy and straightforward as it seems. As long as you remember the slope intercept form of a line, you should have no trouble selecting the correct answer.

(A) f(x) = 4x-2
(B) f(x) = 2x+4
(C) f(x) = -2x-2
(D) f(x) = 1/2x +2
(E) f(x) = -1/2x+1/2

If you remember the slope intercept form of a line (y=mx+b where m is the slope of the line and b is the y intercept) then this problem is very simple. You simply need to look through the answers and select the answer choice with a slope of 2. (A) is incorrect because the slope of the line is 4. (B) works because the slope is 2. (C) has a slope of -2, (D) has a slope of 1/2, and (E) has a slope of -1/2.

The correct answer choice is (B).

On sat.collegeboard.com 64% of the responses were correct.

For more help with math visit www.myknowsys.com.