How can I Change this equation to that equation?

Question

how can i change x/-3.4 + y/-13 = 1 which is in the symmetric equation into the general equation Ax + By + C = 0 ?

In Ax + By + C = 0 what does A stand for, what does B stand for, and what does C stand for?

The reason I am asking is because my book doesn't explain it very well and I didn't understand so that is why I am asking in case you are wondering. Sorry if this is a dumb question.

Thank you for your help in advance

Answer 1

First, you need to rationalize in order to get rid of the denominators of the fractions. To do this, multiply by LCM of the denominators, which in this case is (-3.4)(-13).

Multiplying each component by this number, you get:

(-13)x + (-3.4)y = 1(-3.4)(-13) ------>
-13x - 3.4y = 44.2

Now move everything to left side to get into the form you want.

-13x - 3.4y - 44.2 = 0

Comparing this to Ax + By + C = 0, you can conclude that:

A = -13
B = -3.4
C = -44.2

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Hope this helps

Answer 2

Multiply by the lowest common denominator. In this case, your lowest common denominator is (-3.4)(-13), so multiply ALL terms by that.

x/(-3.4) [(-3.4)(-13)] + y/(-13) [(-3.4)(-13)] = 1(-3.4)(-13)

Note that you now have numbers which cancel. Look at each fraction and notice the numerator and denominator have a common term. These terms cancel out, leaving you with

x(-13) + y(-3.4) = (-3.4)(-13)

The equation of a line in standard form does NOT allow A to be negative, so you have to get rid of that -13 by multiplying -1 all the way through.

13x + 3.4y = 3.4(13)
13x + 3.4y = 44.2
13x + 3.4y - 44.2 = 0

It is perfectly reasonable to not want *any* decimals, so you can multiply the whole equation by 10 if you wish. The reason why you can do that is because the right hand side (0) remains 0, since 0 times anything is 0. So let's multiply everything by 10, shifting the decimal place one to the right.

130x + 34y - 442 = 0

And there you have it.

Answer 3

A, B, and C are just constants that you get from rearranging the initial equation. It's just another form of the equation that will be useful when you learn more theorems in the future.

in this case you would solve it like this:
x/-3.4 + y/-13 = 1
1/-3.4(x) + 1/-13(y) = 1
1/-3.4(x) + 1/-13(y) -1 = 0
so A = 1/-3.4, B= 1/-13, and C= -1

Answer 4

It's not a dumb question. A dumb question is something like "What is 3x if x=4?"

The way to get the answer is:
1) to multiply through both sides to get rid of the denominators, and
2) get everything on one side of the equal sign.

So multiply through by 3.4(13):

(3.4)(13)x/-3.4 + 3.4(13)y/(-13) = (3.4)(13)1

the 3.4 cancels on the x, and the 13 cancels on the y

-13x -3.4y = 44.2

Now add 13x+3.y to both sides and you get

0 = 13x + 3.4y + 44.2

A is the number in front of x (13), B the number in front of y (3.4), and C is the last number (44.2).

You can also multiply through by 10 to get rid of decimals, as someone else suggested.

Answer 5

(1)x/-3.4+(1)y/-13-1=0

A=1 because there is no number in FRONT of x so x is multiplied by itself.
B=1 because there is no number in FRONT of y so y is multiplied by itself
C=-1 because all you have to do is get the one side equal to zero. If you subtract the one from both sides you have your C.

Answer 6

A = -3/4
B =-1/13
C = -1