Subscribe to our YouTube channel for the latest videos, updates, and tips.


Slope of a Straight Line

What is slope of a straight line?

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.

The slope of the line is generally denoted by ‘m’. Thus, m = tan θ. The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ. The slop of a line is positive or negative according as θ is acute or obtuse. Sine a line parallel to x-axis makes an angle of 0° with x-axis, therefore its slope is tan 0° = 0. A line parallel to y-axis that is i.e., perpendicular to x-axis makes an angle of 90° with x-axis, so its slope is tan \(\frac{π}{2}\) = infinity. Also the slope of a line equally inclined with axes is 1 or -1 as it makes 45° or 135° angle with x-axis.

In short, the slope of a line is the trigonometrical tangent of its inclination.

In the above figure the inclination of the lines MN and PQ are α and β respectively.

 

Solved examples to find the slope of a straight line:

1. Find the slope or gradient of a straight line whose inclination to the positive (+ve) direction of x-axis in anticlockwise direction is

(i) 30°

(ii) 0°

(iii) 45°

(iv) 135°

Solution:

(i) 30°

Slope or gradient = tan 30° = \(\frac{1}{√3}\)


(ii) 0°

Slope or gradient = tan 0° = 0


(iii) 45°

Slope or gradient = tan 45° = 1


(iv) 135°

Slope or gradient = tan 135° = -cot 40° = -1



2. What can be said regarding a line if its Slope or gradient is

(i) (+ve)

(ii) Zero (0)

(iii) (-ve)

Solution:

Let ∅ be the angle of inclination of the given straight line with the positive (+ve) direction of x-axis in anticlockwise direction. Then its Slope or gradient is given by m = tan ∅.

(i) Slope or gradient is positive (+ve)

⇒ m = tan ∅ > 0

⇒ ∅ lies between 0° and 90°

⇒ ∅ is an acute angle.


(ii) Slope or gradient is zero (0)

⇒ m = tan ∅ = 0

⇒ ∅ = 0°

⇒ either the line is x-axis or is parallel to x-axis.


(iii) Slope or gradient is negative (-ve)

⇒ m = tan ∅ < 0

⇒ ∅ lies between 0° and 180°

⇒ ∅ is an obtuse angle.

 The Straight Line




11 and 12 Grade Math

From Slope of a Straight Line to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. How to Find the Average? | What Does Average Mean? | Definition

    May 15, 25 06:05 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  2. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More

  3. Worksheet on Rounding Decimals | Questions Related to Round a Decimal

    May 15, 25 11:52 AM

    Worksheet on Rounding Decimals
    The worksheet on rounding decimals would be really good for the students to practice huge number of questions related to round a decimal. This worksheet include questions related

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 14, 25 03:01 PM

    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Rounding Off to the Nearest Whole Number | Nearest 10, 100, and 1000

    May 13, 25 03:43 PM

    Nearest Ten
    Here we will learn how to rounding off to the nearest whole number?

    Read More