tan(x) is an increasing function, where x ∈ (0, 90°).
Hence if \(x_1>y_1\), then slope of AB> slope of KL (where x_1 and y_1 lies between 0 and 90°)
tan(x) is an decreasing function, where x ∈ (90°, 180°).
Hence if \(x_1>y_1\), then slope of AB< slope of KL (where x_1 and y_1 lies between 90° and 180°)
You don't have to find the tan values of the angles to compare the slope.
Another way to compare the slopes is to compare the increment in the y-co-ordinates of both lines, for the equal increment in the x-co-ordinates.
vanam52923 wrote:
VeritasKarishma wrote:
vanam52923 wrote:
Bunuel chetan2uVeritasKarishmaHi, please see the attached image
Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)
AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify
Also same doubt if slope postive
You have to consider the angle made on the positive side of x axis.
Slope is the change in y for every unit increase in x i.e. you go from left to right. If you increase x by 1, what happens to y?
Does it increase by 1? Then slope is 1.
Does it increase by 2? Then slope is 2.
Does it decrease by 1? Then slope is -1
and so on...
Both lines you have drawn have negative slopes because going from left to right, y is decreasing.
thank you for your response.
yes i understand that
But of these two lines which one has a greater slope, how can i answer that without finding tan /sin etc
here AB has greater angle(120) compared to CD(Cd) if i go from left to right , and one which has greate angle has greater slope so in that case Slope of AB >Cd but since bth are negative slopes so absolute value of slope of AB will be more negative compared to CD so in short CD will have greater slope compared to Ab but right answer is AB has greater slope,Can u plz explain.
Also i am ataching pic for postive slope,looking at the pic i can say slope AB >KL as Ab makes greater angle with x axis than KL