Question

angles made by the line with the positive direction of x-axis are given find the slope of these lines 45 degree 60 degree and 90 degree

Answer 1

The tangent value of any trigonometric angle that a straight line makes with the positive direction of the x-axis in anticlockwise direction is called the slope or gradient of a straight line.

The angle of inclination of a line is the angle made by the line with the positive direction of the x-axis. It is usually measured from the positive x-axis in the anti-clockwise direction

Answer 2

Answer:

Angle made with the positive direction of X-axis ($\theta$) = 45°  

The slope of the line (m) = tan $\theta$.

$m = tan(45^0)=1.$

Therefore, the slope of the line is 1.

Angle made with the positive direction of X-axis ($\theta$) = 60°  

The slope of the line ( m ) = tan  $\theta$

$m = tan ( 60^0) = \sqrt{3}$

Therefore, The slope of the line is $\sqrt{3}$.

Angle made with the positive direction of X-axis (   $\theta$ ) = 90°  

The slope of the line (m) = tan $\theta$

$m=tan(90^0)$

The value of  $tan(90^0)$  is not defined.  

Hence slope of the line cannot be determined.