Given Equation AX + BY + C = 0, which following conditions would be true for graph of line to have a negative slope and a postive y-intercept?

Question

A. A>0, B>0, C>0
B. A>0, B<0, C>0
C. A>0, B>0, C<0
D. A>0, B<0, C<0

I cant figure this out!

Answer 1

In this form
Ax + By + C = 0

Slope m = -A/B
y-intercept b = -C/B

You are looking for, a negative slope
Slope m = -A/B

And, a positive y-intercept
C/B

So,
Ax + By - C = 0

Can you answer now?

Answer 2

I still don't get it:\

Is C the y-intercept? or B?

How do I know which one is greater or less? This is mind twisting, i don't get it

Answer 3

I would change it to slope intercept form
y=mx+b

y-a/b x -c/b

so for a negative coefficent of x, both a,b have to be positive, or both have to be negative. A positive y intercept means that c or b has to be negative, but not both.

Answer 4

Ok. That kind of makes sense.

Answer 5

To have a negative slope and positive
y-int, A and B must have the same sign
, C must have the opposite sign.

Therefore, the answer is C.

If the Eq was in this form:
AX + BY = C; A, B, and C must have the
same sign.