The discussion revolves around determining the set of values of m for which the asymptotes of a given curve intersect at a point above the line defined by y=3x-2. The curve is expressed as y=\frac{3(m+1)x+m-2}{(m-2)x+3m}.
Several participants have provided insights into the relationship between the asymptotes and the line, suggesting the need to set up an inequality to compare the y-values at the intersection point and on the line. There is ongoing exploration of the conditions on m, with some participants expressing uncertainty about the next steps.
Participants are working under the constraints of the problem as stated, with some questioning the clarity of the original problem statement regarding the asymptotes. There is a focus on ensuring the conditions derived are valid for the specified intersection criteria.
I believe this should say "such that the asymptotes of the curve..."thereddevils said:Homework Statement
Find the set of values of m such that the asymtote of the curve,
[tex]y=\frac{3(m+1)x+m-2}{(m-2)x+3m}[/tex] intersect at a point above the line y=3x-2
thereddevils said:Homework Equations
The Attempt at a Solution
Vertical asymtote, x=-3m/(m-2)
horizontal asymtote, y=3(m+1)/(m-2)
i am not sure how to move on.
Mark44 said:I believe this should say "such that the asymptotes of the curve..."
The vertical and horizontal asymptotes intersect at (-3m/(m - 2), 3(m + 1)/(m - 2)). For this point to be above the corresponding point on the line y = 3x - 2, what are the conditions on m?
Mark44 said:No, it asks you to find the set of values of m such that the asymptotes of the curve...
intersect at a point above the line y=3x-2.
The two asymptotes intersect at (-3m/(m - 2), 3(m + 1)/(m - 2)). What are the coordinates of the line y = 3x - 2 when x = -3m/(m - 2)?
What are the conditions on m so that the asymptote intersection is above the point on the line at which x = -3m/(m - 2)?
Mark44 said:Set up the inequality with the y value at the point of intersection (of the asymptotes) on one side, and the y value of the line on the other. For both points, use the same x value.