Question

Which of the following options is correct about the given graph.

A. $A$ and $B$ have minimum value of slope
B. $B$ has minimum value of slope
C. $D$ has minimum value of slope
D, $A,B,C$ and $D$ have the same value of slope.

Answer 1

Hint : We are given four rays in the given graph , we have to find the relation between their slopes so that we can check all the options given in the question, the main formula here in the question is the formula for the slope of a line the slope ( $m$ ) of a line is given by,
$m = \tan \theta$

Complete step-by-step answer :
The slope of a line is given by the formula
$m = \tan \theta$
The tan function is increasing in the interval $\left( {0,\dfrac{\pi }{2}} \right)$ , so we can say that the more the angle between the horizontal axis, the more will be the tangent value of that line or segment also the more will be the slope of that line or segment.
The ray A has the smallest angle of ${\theta _1}$ because it is nearer to the horizontal axis. The ray $D$ has the highest angle ${\theta _4}$ . The more the angle, the more the slope so the slope of ray A will be smallest while the slope of ray D will be the largest. The slope of a line is directly proportional to the angle of inclination of the straight line with the positive x axis.
The slopes thus are in the order of
$A < B < C < D$
So, the ray D has the maximum value of slope.
Hence, option (C) is the correct answer to the given problem.
So, the correct answer is “Option C”.

Note : When calculating the slope of a line the angle measured is with the positive side of the horizontal axis. Here more the angle between the line and horizontal axis more is the slope but the opposite will be true when the lines lie in the second quadrant, because in the second quadrant the angle will be made on the negative side of the horizontal $(x)$ axis.