2. SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE scnctg@gmail.com WELCOME TO THE HIGHER MATHEMATICS CLASS

3. Let us enjoy a song Which road is endless? Let us see a picture Which type of the road this is ?

4. THE STRAIGHT LINES Chapter - 3 Exercise - 3.3 Book: Higher Mathematics Panjeree Publications

5. Learning Outcomes After complete this chapter students can 1.Explain straight lines 2.Sketch the graph of straight lines 3.Explain the Slope of straight line 4.Explain Different types straight lines (Till y=mx+c )

6. Definition of Straight Line : The locus of the set of points which maintain always equal distance from two fixed points is called Straight Line.

7. Draw the graph of 2x+3y=12 Solution: Here, 2x+4y=12 Observe the following problem x036-3 y4206 Find the values of y related to the values of x

9. Sketch the Graph of4x-5y-20=0 Here 4x-5y=20 Observe another problem x0-5-105 y-4-8-120 Find the values of y related to the values of x

10. Graph

11. Slope of the Straight line: the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m. The direction of a line is either increasing, decreasing, horizontal or vertical.

12. Equation of Straight lines about Axes Equation of x- axis y=0 Equation of y-axis x=0 Equation which is parallel to x axis y=b Equation which is parallel to y axis x=a N.B. Figure on white board

13. The Equation of st line which passes through the origin and slope is m becomes y=mx The Equation which makes angle with the positive direction x-axis y=xtan

14. A straight line intercepts b from y-axis and slope is m the equation becomes y=mx+b A straight line which makes angle with the positive direction of x –axis and intercepts c from y axis becomes y=xtan +c

15. Group work 1. Draw the graph of 2x+4y=12 2. Draw the graph of 6x-9y=18

16. Evaluation 1 What is slope? 2 Find the value of2x+4y=12 3 If slope=0 then type of the line becomes….? 4 Find the angle with x-axis of 2x+4y=12

17. Home work 1.Draw the graph of 2x+4y=12 and find also the slope and length of interception from both axes 2.Learn all formulae of straight lines

18. Thank you all Euclid, Father of the Geometry