Line A has the equation 3x + y = 7. Which of the following

I first rewrote the equation in the standard y=mx+b form. Therefore, Line A as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.

Thought process next is what line would be perpendicular to Line A? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.

You can also test this by graphing the equation, although I guess this would take more time.

From, y=-3x+7, you get:
x=0, y=7 --> (0,7).
Then from the slope you know that for every 3 down (negative slope) you have one right --> (1,4) etc etc

You can then do the same for the rest of the equations to see it visually. For sure, it will take longer though that just looking for the reciprical slope. But if you don't know this about the slope, then I guess it is better than nothing!

However, it pretty much makes intuitive sense, that a slope of the same sign would not lead to a perpendicular line, since it would follow the same direction. It could cross, but it wouldn't be perpendicular. Right?

Hello everyone this is my first post!

Line A has the equation 3x + y = 7. Which of the following lines is perpendicular to Line A

RULE : If line 'a' with slope m is perpendicular to say a line 'x' with slope n , then m*n = -1 or conversely if two lines a and x with slopes m and n respectively, are such that their slopes m*n = -1 . Then we can say that a and b are perpendicular.

In the question above Line A has the equation 3x + y = 7. => y= (-3)x + 7 (which is of the form y=mx+b where m is the slope). therefore slope of line a is m=-3

so we need to find a line in the options that has a slope n= 1/3 ( since m*n=-1 (prerequisite for being perpendicular) =>-3*n=-1 =>n =1/3)

Almost all the equations below are of the form y=mx+b so its really easy to find the slope (lets call slope n)
(A) y = 3x + 4-------> n=3
(B) y = –3x – 6------->n=-3
(C) y = (1/3)x – 1------->n=1/3 (Eureka we found it!)
(D) y = (–1/3)x + 2------->n=-1/3
(E) y = (–7/3)x – 5-------> we don't really have to even check this..but sometimes I get a little paranoid and check it anyway n=-7/3

so the only option that works is option C

Give me a kudos if I helped you

Thanks

The concept of inverse reciprocal is at play here.
The slope a line perpendicular to another line is always reciprocal and opposite in sign.

Here the slope is -3 {3x+y=7===> y=-3x+7}

therefore the slope of the other line will be -(-1/3)=1/3

Only one option has it C

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