Reminder You have already completed the bridging booklet
Reminder You have already completed the bridging booklet chapter 9 Linear graphs If you need support with any of the following you MUST see your teacher Rearranging a linear equation to find the gradient and intercept Drawing a line from an equation
Linear coord geometry • KUS objectives BAT explore gradients of parallel and perpendicular line BAT rearrange and find equations of lines Starter: Ten questions Identify the equation of each of the following line graphs
Starter: identify linear equations y Identify the equations of these lines x
Answers • • • y = 2 x + 3 y = 2 x - 4 y = 3 x + 1 y = -2 x + 5 y = x + 2 y = 3 y = 4 x y = -x + 1 x = 2 y = -x + 8
Notes: General equation of a line We are used to: gradient y-intercept Another ‘standard way to write the equation of a line is: The General form of the equation of a line
WB 1 gradient and y intercept For each of these equations, i) rearrange it into the form y = mx + c ii) give the gradient iii) give the intercept on the y-axis. Gradient m = -2 Intercept (0, 10) 10 Gradient m = 2. 5 Intercept (0, 3) 3
Notes 1 y y=3 x+1 y=3 x+2 y=3 x+3 y=3 x+4 y=3 x+5 y=3 x– 1 y=3 x– 2 y=3 x– 3 y=3 x– 4 The ‘family’ of Parallel lines with equation y = 3 x + a x
Challenge 1 There are three sets of parallel lines here. Match them up and say what the gradient is for each set.
General equation intersection points Why bother with the general equation? Solve these simultaneous equations: Easier to work with:
General equation intersection points Why bother with the general equation? Solve these simultaneous equations: The solution is the Intersection point of the two lines (-2, -½)
Challenge 2 Which of these lines are parallel to the line 3 x - 2 y – 4 = 0
Notes These lines are perpendicular
Notes What is each gradient? 1 2 Gradient = -2 2 1 Gradient = ½
Notes What is each gradient? 1 3 3 Gradient = -1/3 1 Gradient = 3
Notes 1 THE GRADIENT OF A PERPENDICULAR LINE IS THE NEGATIVE RECIPROCAL OF THE OTHER
y Notes Draw a Perpendicular line to y = 3 x What do you notice? The ‘family’ of Perpendicular lines with general equation y = -1/3 x + a x
Notes We are used to: gradient y-intercept The Perpendicular line has gradient m 2 where: line Examples: 2 -5 perpendicular
Practice 1 What is the gradient of the lines perpendicular to these? y = 2 x + 1 y = 2 + 4 x y = 3 x + 2 y + 2 x = 2 2 y = 3 x - 2 5 y + 2 x = 3 m = 2 m = 4 m = 3 m = -2 m = 3/2 m = -2/5 -1/ = m 2 -1/ = -1/ m 4 -1/ = -1/ m 3 -1/ = 1/ m 2 -1/ = -2/ m 3 -1/ = 5/ m 2
WB 2 Has gradient m 1 = -2 So the gradient of a perpendicular line is m 2 = ½ When x = 4, y = 9 … so
WB 3 Has gradient m 1 = -1/5 So the gradient of a perpendicular line is m 2 = 5 When x = 3/5, y = 7 … so
WB 4 Two points A(1, 2) and B(-3, 6) are joined to make the line AB. Find the equation of the perpendicular bisector of AB First the midpoint of line AB is 2 nd the gradient of line AB is So the perpendicular gradient is When x =1, y = 2 so Is the perpendicular bisector of line AB
KUS objectives BAT explore gradients of parallel and perpendicular line BAT rearrange and find equations of lines self-assess One thing learned is – One thing to improve is –
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