Hi everyone,

I came across a tough problem that I (eventually) figured out, but would like someone to verify that my logic makes sense, or propose a better way of doing the problem.

(OG 12 Diagnostic Test Prob #39)

In the xy-plane, if line k has negative slop and passes through the point (-5, r), is the x-intercept of line k positive?

(1) The slop of the line k is -5
(2) r>0


My way of doing the problem:

1. we know that x intercept would be (x,0)
2. we know that slope of line = (Y1-Y2) / (X1-X2)
3. The equation we're solving becomes slope = (r-0)/(-5-x)

(1) -5 = (r-0)/(-5-x) --> doesn't help, already know that slope is negative, and still have two variables to solve

(2) - slope = (r>0) / (-5-x) --> this tells us that the numerator is positive, so the denominator must be negative.

If x>0, then numerator is negative.
If x=0, then numerator is still negative
If -4<x<0, then numerator still negative

So, since x could be positive or negative or 0, (2) is no good.

Combining the two doesn't tell us anything new.

-5 = (r>0) / (-5-x)

x could still be positive or negative.

thoughts?
-v