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 π2 = 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° = 13


(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. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    May 07, 25 01:48 AM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  2. Dividing Decimals Word Problems Worksheet | Answers |Decimals Division

    May 07, 25 01:33 AM

    Dividing Decimals Word Problems Worksheet
    In dividing decimals word problems worksheet we will get different types of problems on decimals division word problems, dividing a decimal by a whole number, dividing a decimals and dividing a decima…

    Read More

  3. How to Divide Decimals? | Dividing Decimals by Decimals | Examples

    May 06, 25 01:23 AM

    Dividing a Decimal by a Whole Number
    Dividing Decimals by Decimals I. Dividing a Decimal by a Whole Number: II. Dividing a Decimal by another Decimal: If the dividend and divisor are both decimal numbers, we multiply both the numbers by…

    Read More

  4. Multiplying Decimal by a Whole Number | Step-by-step Explanation|Video

    May 06, 25 12:01 AM

    Multiplying decimal by a whole number is just same like multiply as usual. How to multiply a decimal by a whole number? To multiply a decimal by a whole number follow the below steps

    Read More

  5. Word Problems on Decimals | Decimal Word Problems | Decimal Home Work

    May 05, 25 01:27 AM

    Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1

    Read More