M02-27

Question

If in the xy plane line  m  has the equation  y=3x-8 , then line  m  passes through which of the following points?

A. (3, 1)
B. (3, 4)
C. (4, 2)
D. (6, 9)
E. (6, 15)

Bunuel · Answer

Official Solution:

If in the xy plane line  m  has the equation  y=3x-8 , then line  m  passes through which of the following points?

A. (3, 1)
B. (3, 4)
C. (4, 2)
D. (6, 9)
E. (6, 15)

Backsolve. Plug in the value of  x , the first coordinate into the given equation, and check if the value of  y  matches. 
 
For example, start with answer choice (C), (4, 2). If  x = 4 ,   y = 3 * 4 - 8 ,  y = 4 . That does not match 2.
 
For answer choice (A), (3,1), if  x = 3 ,  y = 3 * 3 - 8 = 1 . The answer matches.

Answer: A

IonutCZ · Answer

I think this question is  good  and  helpful .

_shashank_shekhar_ · Answer

best way to put the values of x and y from the options in the equation-
1) x=3x=3 , y=3∗3−8=1
Ans- A

dine5207 · Answer

such an easy pesy question

LeoN88 · Answer

My approach, put the x-coordinate in the given equation and find whether the answer is matching the y-coordinate.

y=3x-8, putting x=3 we are getting y=1. So A. (3, 1) satisfies the equation. This point is on the line m.

Godsent · Answer

Good and easy question

Posted from my mobile device

nishatfarhat87 · Answer

Hi Bunuel,

I was trying to find the x and y intercept and the answer wasn't matching the solution. Why is my way incorrect? Can you please explain.

Bunuel · Answer

Why do you need to find x and y-intercept? Also, you forgot to write down your approach.

Vihar123 · Answer

Why cant we find the points by first plugging in X=0, and then Y=0?

Bunuel · Answer

Putting x = 0, you find the y-intercept of the line. So, the point at which the line crosses y-axis.
Putting y = 0, you find the x-intercept of the line. So, the point at which the line crosses x-axis.

Is this what the question is asking?

TheNightKing · Answer

If a line passes through a point then the equation of that line should satisfy the point.

y=3x-8

A. (3, 1) -> x=3 gives us y=9-8=1. Works
B. (3, 4) -> x=3 gives us y=9-8=1. Does not work
C. (4, 2) -> x=4 gives us y=12-8=4. Does not work
D. (6, 9) -> x=6 gives us y=18-8=10. Does not Work
E. (6, 15) -> x=6 gives us y=18-8=10.Does not Work

Answer A

GKomoku · Answer

hello Bunuel in this type of question (in the future time) once we start to backsolve the question and option (A) matches, should we double-check and verify that the rest four is wrong or we can mark (A) and go ahead? what are your suggestions?

Bunuel · Answer

There is only one correct answer in PS questions, so if you got it, and are 100% sure that you did not make mistake then you can ignore other options.

nisthagupta28 · Answer

Please check why my answer is incorrect. 
Tried to find the y-intercept = (0,-8)
The slope is 3. 
I was trying to find another point that will give the same slope - using the rise/run formula.
However, Incorrect answer. 
Please help as to what is wrong with the approach?

The approach by @brunnel is very simple and straightforward, however, it might not be my first approach in other question.

Bunuel · Answer

Given two points  (x_1,y_1)  and  (x_2,y_2)  on a line, the slope  m  of the line is:

m=\frac{y_2-y_1}{x_2-x_1}

So, we have m = 3 and one of the points is (0, -8).

3=\frac{-8-y_1}{0-x_1} . Now, plugging options should give correct answer. A (3, 1) works:  3=\frac{-8-1}{0-3}=-\frac{9}{-3}=3

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