Answer

Verified

389.7k+ views

**Hint:**Slope at a point of a curve (function) is equal to the tan of the angle that the tangent to the curve at that point makes with positive x-axis. If two lines are perpendicular to each other then the slopes of the two lines are negative reciprocals of each other.

**Complete step-by-step solution:**

Let us first understand what is meant by slope of a function. Slope at a point of a curve (function) is equal to the tan of the angle that the tangent to the curve at that point makes with positive x-axis.

A line is a curve that has a constant slope or we can say that a line is a curve that has equal slope at all the points.

If two lines are perpendicular to each other then the slopes of the two lines are negative reciprocals of each other. If the slopes of the two lines are ${{m}_{1}}$ and ${{m}_{2}}$ respectively, then the two slopes are related as ${{m}_{1}}{{m}_{2}}=-1$ or ${{m}_{1}}=-\dfrac{1}{{{m}_{2}}}$ ….. (i)

It is given that there are two lines perpendicular to each. One of the lines has a slope of $-\dfrac{1}{3}$ .

This means that ${{m}_{1}}=-\dfrac{1}{3}$.

Then by equation (i) we get that ${{m}_{2}}=-\dfrac{1}{{{m}_{1}}}=-\dfrac{1}{\left( \dfrac{-1}{3} \right)}$

$\Rightarrow {{m}_{2}}=3$

Therefore, the slope of the line that is perpendicular to the line having a slope of $-\dfrac{1}{3}$ is equal to 3.

**Note:**Note that we two lines are perpendicular to each other, the angle of one of the lines with the positive x-axis must be acute and the angle of the other line with positive x-axis must be obtuse. We can also see in this the given question. When the angle is acute, slope is positive and when the angle is obtuse, the slope is negative. This helps us in checking whether our answer is correct or not.

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

10 examples of law on inertia in our daily life

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths