Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines. (1) 45° (2) 60° (3) 90°

Explanation:- 

The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. When we have the angle made by the line with the positive direction of the X-axis, we can use trigonometric functions to find the slope of the line.

Let’s consider each angle given:

(1) 45°: A line that makes an angle of 45° with the positive direction of the X-axis forms an isosceles right triangle with the X-axis. The tangent of this angle is equal to the ratio of the opposite side to the adjacent side of this triangle. Therefore, the slope of the line that makes an angle of 45° with the positive direction of the X-axis is 1.

(2) 60°: A line that makes an angle of 60° with the positive direction of the X-axis forms an equilateral triangle with the X-axis. The tangent of this angle is equal to the ratio of the opposite side to the adjacent side of this triangle. Therefore, the slope of the line that makes an angle of 60° with the positive direction of the X-axis is √3.

(3) 90°: A line that makes an angle of 90° with the positive direction of the X-axis is a vertical line, and it has an undefined slope because the change in the x-coordinate between any two points on this line is zero. Thus, the denominator of the slope formula is zero, which makes the slope undefined.

Therefore, the slope of the line that makes an angle of 45° with the positive direction of the X-axis is 1, the slope of the line that makes an angle of 60° with the positive direction of the X-axis is √3, and the slope of the line that makes an angle of 90° with the positive direction of the X-axis is undefined.