SOLUTION: 3. Given the two points (a/3, b/3) and (3/a, b) a)Find the slope of the line between the two points. b)When is the slope negative? ______;When is the slope positive? _______

Algebra ->  Trigonometry-basics -> SOLUTION: 3. Given the two points (a/3, b/3) and (3/a, b) a)Find the slope of the line between the two points. b)When is the slope negative? ______;When is the slope positive? _______       Log On


   

Question 1190624: 3. Given the two points (a/3, b/3) and (3/a, b)
a)Find the slope of the line between the two points.
b)When is the slope negative? ______;When is the slope positive? _______ When is the slope zero? ______; When is the slope undefined? ________
c)Find the distance between these two points when a = 1 and b = 1.
Answer by chitrank(4) About Me  (Show Source):
You can put this solution on YOUR website!
The slope would be %28b-b%2F3%29%2F%283%2Fa-a%2F3%29. Which is %282b%2F3%29%2F%28%289-a%5E2%29%2F3a%29, which if you further simplify would be %282b%2A3a%29%2F%283%2A%289-a%5E2%29%29 or 2ab%2F%289-a%5E2%29

When is the slope positive? Only when both numerator and denominator of this fraction would be "of the same sign". There are two cases-
Case-1) Both the numerator and denominator are positive. But if 9-a%5E2 has to be positive then a%5E2+%3C+9 or -3%3Ca%3C3. Coming onto the numerator, 2ab, it can be positive only when both a and b are of the same sign. But we found earlier that denominator can be positive only when -3%3Ca%3C3. That means, when -3%3Ca%3C0, b%3C0, and when 0%3Ca%3C3, b%3E0.
Similalry you can solve the second case when Both numerator and denominator has to be negative.
Similar analysis can be done to find out conditions for negative slope.
What about zero slope? That can only happen when the numerator or 2ab is 0, or in other words, a=0 or b=0 or both. But wait! Also check that the denominator does not become 0! Otherwise the slope would become undefined. (Remember you cannot divide with 0?) I hope this would also answer the last remaining question of when is slope undefined.