Slope of a Line

We will discuss here about the slope of a line or gradient of a line.

Concept of slope (or gradient):

If θ (≠ 90°) is the inclination of a straight line, then tan θ is called its slope or gradient. The slope of any inclined plane is the ratio between the vertical rise of the plane and its horizontal distance.

Concept of Slope

i.e., slope = \(\frac{vertical rise}{horizontal distance}\) = \(\frac{AB}{BC}\) = tan θ

Where θ is the angle which the plane makes with the horizontal

Slope of a straight line:

The slope of a straight line is the tangent of its inclination and is denoted by letter ‘m’ i.e. if the inclination of a line is θ, its slope m = tan θ.


Note:

(i) The slope of a line is positive if it makes an acute angle in the anti-clockwise direction with x-axis.

Positive Slope

Inclination θ = 45°

Therefore, slope = tan 45° = 1

Negative Slope

Inclination θ = 135° or -45°

Therefore, slope = tan (-45°) = - tan 45° = -1

(ii) The slope of a line is negative, if it makes an obtuse angle in the anti-clockwise direction with the x-axis or an acute angle in the clockwise direction with the x-axis.

(iii) Since tan θ is not defined when θ = 90°, therefore, the slope of a vertical line is not defined. i.e., slope of y-axis is m = tan 90° = ∞ i.e., not defined.

(iv) Slope of x-axis is m = tan 0° = 0.

(v) Since the inclination of every line parallel to x-axis is 0°, so its slope (m) = tan 0° = 0. Therefore, the slope of every horizontal line is 0.

 Equation of a Straight Line






10th Grade Math

From Slope of a Line to HOME




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. Worksheet on Money | Conversion of Money from Rupees to Paisa

    Dec 03, 24 01:29 AM

    Worksheet on Money
    Practice the questions given in the worksheet on money. This sheet provides different types of questions where students need to express the amount of money in short form and long form

    Read More

  2. 2nd Grade Money Worksheet | Conversion of Money | Word Problems

    Dec 03, 24 01:19 AM

    Match the following Money
    In 2nd grade money worksheet we will solve the problems on writing amount in words and figures, conversion of money and word problems on money. 1. Write T for true and F for false. (i) Rs. is written…

    Read More

  3. Subtraction of Money | Subtraction with Conversion, without Conversion

    Dec 02, 24 01:47 PM

    Subtraction of Money
    In subtraction of money we will learn how to subtract the amounts of money involving rupees and paise to find the difference. We carryout subtraction with money the same way as in decimal numbers. Whi…

    Read More

  4. Word Problems on Addition of Money |Money Word Problems|Money Addition

    Dec 02, 24 01:26 PM

    Word Problems on Addition of Money
    Let us consider some of the word problems on addition of money. We have solved the problems in both the methods i.e., with conversion into paise and without conversion into paise. Worked-out examples

    Read More

  5. Addition of Money | Add The Amounts of Money Involving Rupees & Paisa

    Nov 29, 24 01:26 AM

    3rd Grade Addition of Money
    In addition of money we will learn how to add the amounts of money involving rupees and paisa together. We carryout with money the same way as in decimal numbers. While adding we need to follow that t…

    Read More