Answer:
D
Step-by-step explanation:
So we have the equation:
[tex]ax+by+c=0[/tex]
First, let's convert this to slope-intercept form.
Subtract ax from both sides:
[tex]by+c=-ax[/tex]
Subtract c from both sides:
[tex]by=-ax-c[/tex]
Divide everything by b:
[tex]y=-\frac{a}{b}x-\frac{c}{b}[/tex]
We are told that a>0, b<0, and c>0.
In other words, a is positive, b is negative, and c is positive.
The slope of the equation is -a/b.
Since a is positive and b is negative, we will have:
-(+)/(-).
The negatives will cancel out. Therefore, our slope will be positive.
Since our slope is positive, our line must be upwards sloping. Eliminate answers A and C.
Also, our y-intercept is:
-c/b.
c is positive and b is negative. Thus, similarly:
-(+)/(-).
Again, the negatives cancel. This means that the y-intercept must be positive.
Out of B and D, the graph that has a positive y-intercept is D.
D is our answer :)
