Question

Find the slope of the line making an inclination of \[{{60}^{\circ }}\] with the positive direction off the x-axis.

Answer 1

Hint: Use the fact that the slope of the line can also be represented as the in terms of the tangent of the angle which the line makes with the positive x-axis when going anticlockwise from the x-axis.
 The value of m gives the slope of the line and then equate it to the tangent of the angle which the line makes with the positive x-axis when going anticlockwise from the x-axis as follows
\[m=\tan \theta \]
(Where \[\theta \] is the angle that the line makes with the positive x-axis when going anticlockwise from the x-axis and m is the slope of the line which is inclined to the x-axis with the mentioned angle)
Now, in this question, we will simply put the value of angle that is given in the question and then we will get the value of the slope on taking or finding the tangent of that angle.

Complete step by step answer:
As mentioned in the question, we have to find the slope of the line which makes \[{{60}^{\circ }}\] angle with the x-axis when going anticlockwise from the x-axis.
We know that the slope of the line can be calculated as follows
\[\begin{align}
  & \Rightarrow m=\tan \theta \\
 & \Rightarrow m=\tan {{60}^{\circ }} \\
 & \Rightarrow m=\sqrt{3} \\
\end{align}\]

Hence, the slope of the line which makes the mentioned angle with the x-axis, is \[\sqrt{3}\] .

Note: The students can make an error if they don’t know about the formulae that are given in the hint as without knowing them one can never get to the correct answer.
Other formula that can be used to find the equation of a line is as follows
\[\dfrac{y-{{y}_{1}}}{x-{{x}_{1}}}=m\], where \[\left( {{x}_{1}},{{y}_{1}} \right)\] is the point through which the line passes and it is a known point and m is the slope of this line. also, if we have a slope say y=f(x), then another way of finding slope is we can derive function f(x), with respect to x, which will be slope of function f(x) that is slope of curve f(x) is equal to $\dfrac{d}{dx}[f(x)]$. Also, it is important to know the basic values and the basic properties of trigonometric functions for solving this question as without knowing them one can never get to the correct answer. Try not to make any calculation errors.