1. 1: Straight Lines and Gradients © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

2. Perpendicular Lines  The gradient of the straight line joining the points and is

3. Perpendicular Lines Gradient of black line = Gradient of red line = 3 2 2 –3 Perpendicular Lines Flip the gradient and change the sign

4. Perpendicular Lines Flip the gradient and change the sign to find the perpendicular gradient ie gradient perpendicular to m is – So gradient perpendicular to m = 3 is m = –  So gradient perpendicular to m =  is m = –  If two lines are perpendicular then m 1  m 2 = –1

5. Perpendicular Lines  Parallel and Perpendicular Lines  They are parallel if  They are perpendicular if If 2 lines have gradients and, then:

6. Perpendicular Lines We don’t usually leave fractions ( or decimals ) in equations. So, multiplying by 2 : e.g.Find the equation of the line perpendicular to passing through the point. Solution: The given line has gradient 2. Let Perpendicular lines: Equation of a straight line: on the line

7. Perpendicular LinesExercise Solution: So, Solution: So, 1.Find the equation of the line parallel to the line which passes through the point. Parallel line is has a gradient of –2 2.Find the equation of the line through the point (1, 2), perpendicular to the line

8. Perpendicular Lines

9. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

10. Straight Lines and Gradients  They are parallel if  They are perpendicular if  If 2 lines have gradients and, then:  Equation of a straight line  Gradient of a straight line where and are points on the line where m is the gradient and c is the intercept on the y -axis SUMMARY

11. Straight Lines and Gradients Solution: First find the gradient: e.g. Find the equation of the line through the points Now on the line: Equation of line is

12. Straight Lines and Gradients We don’t usually leave fractions ( or decimals ) in equations. So, multiplying by 2 : e.g.Find the equation of the line perpendicular to passing through the point. Solution: The given line has gradient 2. Let Perpendicular lines: Equation of a straight line: on the line