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?
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!
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?
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
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.
Ok. That kind of makes sense.
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.
To determine the conditions for a line to have a negative slope and a positive y-intercept, we should analyze the given equation in the standard form: AX + BY + C = 0. In this form, the coefficient of X represents the slope of the line, while the constant term represents the y-intercept.
Let's analyze each option to determine which one satisfies the given conditions:
A. A > 0, B > 0, C > 0
Here, A is positive, which means the slope of the line is positive. Therefore, this option does not satisfy the condition of having a negative slope.
B. A > 0, B < 0, C > 0
In this option, A is positive and B is negative. Therefore, the slope of the line would be negative. However, the condition for a positive y-intercept is not met because C is positive.
C. A > 0, B > 0, C < 0
In this option, A and B are positive, which aligns with the condition of having a positive slope. Additionally, C is negative, which indicates that the y-intercept is positive. Thus, this option satisfies the conditions of a negative slope and a positive y-intercept.
D. A > 0, B < 0, C < 0
Here, A is positive, but both B and C are negative. While this option satisfies the condition of a negative slope, the y-intercept would be negative due to C being negative.
Therefore, the correct answer is option C.