RD Sharma Solution for Class 11 - Chapter 23 Lines - Exercise 23.19

RD Sharma is a renowned mathematics author, known for his excellent books that provide solutions to various problems in mathematics. The 11th Class RD Sharma book is one of the best mathematics books for high school students in India.

In Chapter 23 of this book, RD Sharma covers the topic of lines, which is one of the fundamental concepts of geometry. Exercise 23.19 is a set of problems related to the equation of lines in standard form, slope-intercept form, and point-slope form.

Here is a brief overview of the exercise:

Exercise 23.19

1. Write the equation of a line that passes through the point (5, 4) and has a slope of 3.
2. Write the equation of a line that passes through the points (2, -1) and (4, 5) in slope-intercept form.
3. Write the equation of a line that passes through the point (2, 1) and is parallel to the line y = 3x - 4.
4. Write the equation of a line that passes through the point (-1, 6) and is perpendicular to the line y = -2x + 3 in slope-intercept form.

RD Sharma provides step-by-step solutions to each of these problems, along with additional exercises to reinforce the concepts covered.

Here is an example solution provided by RD Sharma for problem 1:

Solution to Problem 1

Given point: (5, 4)

Given slope: 3

The equation of a line with slope m and passing through point (x1, y1) is given by the point-slope form:

y - y1 = m(x - x1)

Substituting the given values, we get:

y - 4 = 3(x - 5)

Expanding the equation, we get:

y - 4 = 3x - 15

y = 3x - 11

Therefore, the equation of the line is y = 3x - 11.

RD Sharma provides detailed explanations and step-by-step solutions for each of the problems in Exercise 23.19, making it easy for students to understand and apply the concepts covered.

Overall, the RD Sharma Solution for Class 11 - Chapter 23 Lines - Exercise 23.19 is an excellent resource for high school students looking to improve their knowledge of lines and equations. With its clear explanations and comprehensive coverage of the topic, this book is a must-have for any student of mathematics.