NCERT Solutions for Class 11 Maths Chapter 9 Exercise 9.1 Straight Lines  PDF Download
JEE Mains & AdvancedNCERT solutions for class 11 maths chapter 9 exercise 9.1 Straight Lines is based on slope of a line. You will learn the coordinates of a point in relation to the fixed point called the ‘Origin’. You can draw the shape by knowing the coordinates of the points in the vertices. You can also figure out its size by figuring out the length of its sides. This way, you can figure out the area or the perimeter of the shape. This exercise also includes essential questions based on finding a line’s slope. The problems can ask students to determine whether two lines are parallel or perpendicular to each other, as well as the angle between two intersecting lines.
Ex 9.1 class 11 maths chapter 9 is composed of 11 questions, some questions are short answer type and some of them are long answer questions. eSaral's subject experts provide class 11 maths chapter 9 exercise 9.1 NCERT solutions, which are designed to assist students in reenacting concepts they have learned in previous classes and solving questions using a different method. It is important to practice with ex 9.1 class 11 maths solutions to score high marks in exams. These solutions are also available in PDF format at eSaral which you can download for free and enhance your learning for preparing this chapter. Download the NCERT solutions PDF from the link given below.
Topics Covered in Exercise 9.1 Class 11 Mathematics Questions
Ex 9.1 class 11 maths ch 9 covers topics like slope of a line, its applications and properties of straight lines. Check the detailed solutions given below.
1. 
Slope of a Line 
2. 
Slope of a line when coordinates of any two points on the line are given 
3. 
Conditions for parallelism and perpendicularity of lines in terms of their slopes 
4. 
Angle between two lines 

Slope of a Line
A line in a coordinate plane forms two angles with the xaxis, which are supplementary to each other. The angle (say) θ made by the line l with positive direction of xaxis and measured anticlockwise is called the inclination of the line.
If θ is the inclination of a line l, then tan θ is called the slope or gradient of the line l.
The slope of a line whose inclination is 90° is not defined.
The slope of a line is denoted by m.
Thus, m = tan θ, θ ≠ 90°

Slope of a line when coordinates of any two points on the line are given
The slope m of the line through the points (x _{1} , y_{1} ) and (x _{2} , y_{2} ) is given by
m = $\frac{y_2y_1}{x_2x_1}$

Conditions for parallelism and perpendicularity of lines in terms of their slopes
Parallel Lines
In a coordinate plane,let nonvertical lines l_{1 } and l_{2} have slopes m_{1} and m_{2} , respectively. Let their inclinations be α and β, respectively
If the line l_{1 } is parallel to l_{2} , then their inclinations are equal
Hence α = β,
tan α = tan β and m_{1} = m_{2}
slope of line l_{1} = slope of line l_{2}
The slope of the lines is equal if the lines are parallel to each other.
Perpendicular Lines
If the lines l_{1} and l_{2} are perpendicular, then β = α + 90°. Therefore, tan β = tan (α + 90°)
if m_{1} m_{2} = – 1,
tan α tan β = – 1
Then tan α = – cot β = tan (β + 90°) or tan (β – 90°)
Therefore, α and β differ by 90°.
Thus, lines l_{1} and l_{2 }are perpendicular to each other.
Two nonvertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

Angle between two lines
The inclination of two lines l_{1}, l_{2} be α_{1} and α_{2 }and α_{1}α_{2}≠ 90°
The slopes of the lines are m_{1 }= tan_{1} and m_{2} = tanα_{2}
Suppose θ is the angle between the lines
tan θ = tan (α_{2 }– α_{1} ) = $\frac{\tan a_2\tan a_1}{1+\tan a_1 \tan a_2}=\frac{m_2m_1}{1+m_1 m_2}$ , as 1 + m_{1}m_{2} ≠ 0
Tips for Solving Exercise 9.1 Class 11 Chapter 9 Straight Lines
We suggest the students have the right orientation to comprehend the questions in NCERT solutions class 11 maths chapter 9 ex 9.1. Here, our expert teachers of mathematics have provided useful tips and tricks to solve exercise 9.1 questions.

This exercise involves the utilization of multiple formulas, so it is recommended that students create a formula chart to gain a better comprehension of the concepts.

Students must solve problems which are provided in NCERT solutions by eSaral. By solving these problems, students will find the straight line slope and how to graphically interpret the answer.

Before solving ex 9.1 questions students must solve examples given before the exercise to be wellversed with the questions and concepts.
Importance of Solving Ex 9.1 Class 11 Maths Chapter 9 Straight Lines
It is essential for students to solve exercise questions to get the most of the topics included in the chapter. Here, we have covered the most important benefits of solving questions of ex 9.1 class 11 maths chapter 9 straight lines.

Solving ex 9.1 questions will provide you the fundamentals of slope of a line and its applications that will give you conceptual understanding of concepts.

The PDF version of this exercise has questions with their answers that will help you to prepare for the exam.

Ex 9.1 class 11 maths chapter 9 has questions in different levels that will provide you a clear and precise understanding of every concept. This will build your selfconfidence in the examination.

By revising the concepts and important questions of ex 9.1 class 11 maths ch 9 solutions, you can improve your speed and accuracy of solving problems.
Frequently Asked Questions
Question 1. What is the inclination of a line 'l' in NCERT solutions class 11 maths chapter 9?
Answer 1. The angle made by the line l with positive direction of xaxis and measured anticlockwise is called the inclination of the line.
Question 2. What do you mean by slope of a line?
Answer 2. If θ is the inclination of a line l, then tan θ is called the slope or gradient of the line l.
Click here to get examready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.