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RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines (Ex 23.7) Exercise 23.7

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Last updated date: 17th Apr 2024
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RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines (Ex 23.7) Exercise 23.7 - Free PDF

Free PDF download of RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines Exercise 23.7 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 23 - The Straight Lines Ex 23.7 Questions with Solutions for RD Sharma Class 11 Maths to help you to revise the complete Syllabus and Score More marks. 

Competitive Exams after 12th Science

Straight Lines

A straight line is a line that does not have any curves in it and it can either have a length or it can be infinitely long. A straight line is a geometrical figure formed when we join two points in a plane with the shortest possible distance between them. Like a Line itself, a straight line doesn't have any width or breadth. Straight lines need not have a definite beginning or end.  A straight line also doesn't have a curve in it. It can either be horizontal, vertical or an oblique or slanted line. If we try to draw out an angle between any two points on a straight line, it comes out to be a 180 degrees angle. 


Types of Straight Lines

A Straight line can be of various forms or types. The straight lines are generally classified based on their alignment. This alignment refers to the angle they form with the x-axis or the y-axis in a cartesian plane. According to the alignment of straight lines, they can be classified as the following types:

  • Horizontal lines

  • Vertical lines

  • Oblique or Slanted lines

 

The Horizontal Line

The line is a horizontal line when it is parallel to the x-axis and perpendicular to the y axis in a cartesian plane. It can also be defined by the angle it makes with the x-axis and the y axis. If the given line makes a 90-degree angle with the y axis and a 0-degree angle with the x-axis, the line can be classified as a horizontal line. 

 

The Vertical Line

The line is a vertical line when it is parallel to the y axis and perpendicular to the x-axis in a cartesian plane. It can also be defined by the angle it makes with the x-axis and the y axis. If the given line makes a 90-degree angle with the x-axis and a 0-degree angle with the y axis, the line can be classified as a horizontal line. 

 

The Oblique or Slanted Line

The lines which make angles with both the x-axis and the y axis are known as oblique or slanted lines. The lines which form angles other than 0 degrees, 90 degrees, 270 degrees and 360 degrees with both the axes can be called oblique or slanted lines. 

 

Types of Slopes

The slope of a line is defined as the angle formed by a line with a positive x-axis. Different kinds of lines from different angles with the x-axis. Slopes can either be positive, negative, infinite or even 0. 

 

Equation of a Straight Line

The equation of a straight line is always a linear equation. Based on the known available information regarding the variables, the angles, and the constants, a straight line in a cartesian plane can have different representations. The direction of a straight line and how steep the line could be is defined by the slope of the straight line.  The slope is calculated as the difference in y coordinates divided by the difference in x coordinates.

 

 An equation of a straight line can be of various forms. These forms are as follows:

  • The general equation of a straight line

  • The slope and y-intercept form of a straight line

  • Slope point form of a straight line

  • Two-point form of a straight line 

  • Intercept form of a straight line

FAQs on RD Sharma Class 11 Solutions Chapter 23 - The Straight Lines (Ex 23.7) Exercise 23.7

1. What is the general equation of a straight line?

If a,b and c are the constants, x and y are the variables and the slope is -a/b, the general equation of a straight line can be given as ax + by + c = 0. For example, 2x + 3y + 6 = 0 is a general equation of the straight line where 2, 3 and 6 are the constants, x and y are the variables and the slope is -a/b which in this case results in -⅔.

2. What is the slope and y-intercept form of a straight line?

A straight line that has a slope equal to tanθ, where θ is the angle formed by the given line with the positive x-axis and the y-intercept, say b can be given by y = mx + b, where m is the slope of the line. 

3. What is the slope point form of a straight line?

A straight line that has a slope equal to tanθ where θ is the angle formed by the given line with the positive x-axis, and when it is passing through a point (x1, y1), the slope-intercept form of a straight line can be given by (y2 - y1) = m(x2 - x1).

4. What is the best way to prepare for Class 11 Chapter 23?

Students must study their notes obtained in class to prepare for the class 11 chapter 23 maths. Students can also use other online sources to understand the concepts given in the chapter. Vedantu is a wonderful online learning app for the students to clear their concepts about any topic and go all types of the study materials in the form of PDF, which is available free of cost.  

5. What is the intercept form of a straight line?

A straight line which has x-intercept as ‘a’ and y-intercept as ‘b’ where point A is on the x-axis and point B is on the y-axis, is given in the intercept form equation by x/a + y/b = 1.