Which of the following equations represents a line

[khushbumerchant]

Which of the following equations represents a line that is
perpendicular to the line described by the equation 3x + 4y = 8 ?

A. 3x + 4y = 18
B. 3x - 4y = 24
C. 4y - 3x = 26
D. 1.5y + 2x = 18
E. 8x - 6y = 24

Source: MGMAT prep test

[RonPurewal]

Hi,
Don't just post a problem without any commentary. The problems come with detailed answer keys, so, in that case, our best response is "Check out the answer key, please".

If you're going to post a problem here, please ask about specifics.
- What do you already understand?
- What don't you understand?
- What method(s) have you tried? Where did you get stuck?
And so on.

Thanks.

[khushbumerchant]

OK Got it.
My problem was that my slope of line "3x + 4y = 8" was not getting a match. Hence I posted it here to know how was the solution different from mine.
However, I re-did it and found the answer.

I am doing it here again, please point out, if you notice any error.

Slope of line: 3x + 4y = 8 is;
4y = -3x + 8
y = -3/4x + 2

So slope of line is -3/4. Therefore the slope of perpendicular line is 4/3

1) 3x + 4y = 18
4y = -3x + 18
y = -3/4x + 9/2 Slope is -3/4 so Incorrect

2) 3x - 4y = 24
-4y = -3x + 24
y = 3/4x - 6 Slope if 3/4 so Incorrect

3) 4y - 3x = 26
4y = 3x + 26
y = 3/4x + 13/2 Slope if 3/4 so Incorrect

4) 1.5y + 2x = 18
1.5y = -2x + 18
y = -2/1.5x + 18/1.5 Slope is in decimal so Incorrect

5) 8x - 6y = 24
6y = 8x - 24
y = 4/3x - 4 Slope is 4/3 so Correct

[tim]

Looks good! Let us know if you have any further questions on this one.

[RonPurewal]

If you totally forget how this sort of thing works"”"”or if you just never learned it in the first place"”"”you can also draw the actual lines.

- You get graph paper on test day. (The plastic drawing boards have grid lines on them.)

"- You can quickly graph each line by letting x = 0 (and solving for y) and then letting y = 0 (and solving for x).
For instance, the line in choice A contains the points (0, 4.5) and (6, 0).

"- Then you can look at the lines you get.
Lines A and D will very clearly not be perpendicular to the original line.
Lines B and C will be closer, but still not perpendicular. (You can also notice that these lines are parallel to each other. So, either (i) both of them are parallel to the original line, or (ii) neither of them is. But it's impossible to have 2 correct answers"”so, (ii) it is.)
Only line E should look parallel to the original line.