Share straight lines Presentation (3).pptx

This is actually a demonstration of the straight lines. This would be really helpful for the students of 11th standard. Though my presentation may not be fully clear, it definitely covers the main concepts associated with this topic. So students, I would be happy if this can be of any help to you all....thank you so much😊😊

1. Straight Lines Name – Aradhya Mukherjee Student Code – BWU/BAG/23/063 Programme Name — B.Sc (H) in Agriculture Course Name – Elementary Mathematics Course Code – RC-BAG102

2. CONTENTS : Introduction Equation of a straight line Slope-intercept form Point-slope form Two- point form Distance formula Intercept form Angle between two lines Slope for two parallel lines Slope for two perpendicular lines Perpendicular Distance between two straight lines

3. INTRODUCTION A line that extends to both sides to infinity and has no curves is called a  straight line . In the classrooms, straight lines are drawn on the floor, the entrance, the window, and the zebra crossing on the roadside .

4. EQUATIONS OF A STRAIGHT LINE The general equation of a straight line is given below: ax + by + c = 0  Where x and y are variables, a, b, and c are constants.

5. SLOPE – INTERCEPT FORM The equation of a straight line in slope-intercept form is given by: y = mx + c Here, m denotes the slope of the line, and c is the y-intercept.

6. POINT – SLOPE FORM The point slope form  formula of equation of a straight line  is given by: y – y 1  = m(x – x 1 ) Here, m = Slope of the line (x 1 , y 1 ) = Point through which the given line passes

7. TWO – POINT FORM Let the given points be A (x 1 , y 1 ), B (x , 2 , y 2 ) and P (x, y) be any point on the straight line joining the points A and B. Then the formula is given by: (y-y1)={(y2-y1)/(x2-x1)}(x-x1)

8. DISTANCE FORMULA Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x 2  – x 1 )² + (y 2  – y 1 )²).  This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

9. INTERCEPT FORM The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. 

10. ANGLE BETWEEN TWO STRAIGHT LINES If θ is the angle between two intersecting lines defined by y 1 = m 1 x 1 +c 1  and y 2 = m 2 x 2 +c 2,  then, the angle θ is given by tan θ=±( m 2 -m 1 ) / (1+m 1 m 2 )

11. SLOPE FOR TWO PARALLEL LINES The slope of parallel lines is always equal.   Parallel lines have the same slope because their rise over run ratio is equal. They make an equal angle with the positive x-axis. If we have two slope m1 and m2 for two parallel lines 1 and 2, then m1 = m2.

12. SLOPE FOR TWO PERPENDICULAR LINES Slope of perpendicular lines are such that the slope of one line is the negative reciprocal of the slope of another line. If the slopes of the two perpendicular lines are m 1 , m 2 , then we can represent the relationship between the slope of perpendicular lines with the formula m 1 .m 2  = -1.

13. PERPENDICULAR DISTANCE BETWEEN STRAIGHT LINES Two lines are parallel to each other if the distance between them at any point remains the same . The distance between two parallel lines is calculated by the  distance of point  from a line. It is equal to the length of the perpendicular distance from any point to one of the lines. the distance between two lines is: d =|Ax 1  + By 1  + C| / (A 2  + B 2 ) ½ .