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y
Starter
5
1) Plot and join these coordinates
A(3,4) B(2,-4) C(-3,2)
4
2) What is the gradient of line AB
3
2
3) What is the length of line BC
4) Find the coordinates of the
midpoint of line AC
5) Is the triangle isosceles? Why?
1
– 4
– 3
– 2
– 1
– 1
– 2
– 3
6) Sketch
a) y  0.5x  2
b) 3x  2 y  6  0
– 4
– 5
1
2
3
4
x
Rearranging equations A
Theta
p132 Ex 16.5
#1 & 2
Rearranging an equation into the form y = mx + c helps sketching or
finding the gradient
Rearrange & find the gradient for:
1)
2y  6  4x  0
4)
2x  3 y  6  0
2)
3x  2 y  6
5)
3x  2 y  7  0
3)
8x  2 y  9  0
6)
x  5y  4
Rearranging equations B
Theta
p133 Ex 16.6
p140 Ex 16.14
Rearranging an equation into the form ax + by + c = 0 helps to find the
intercepts easily and avoids fractional values (more elegant)
Rearrange & find the intercepts for:
1)
2)
3)
y  4x  5
4)
4x
y
5
3
5)
x 5
y

3 4
y  2 x  7
y
2x  4
3
6– 6
1
2
3
4
5
1
2
3
4
5
1– 5
2
3
4
5
1
2
3
4
Starter
y
Sketch these graphs
1) y = 2x – 4
2) x = 4
2x
y


3
4)
3
3) y = – x
2
5) y  5 x  2
6) y  4 
x
3
Write the equation for these lines:
y
6
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
– 3– 2– 1
– 1
1
2
3
4
5
6
x
– 3– 2– 1
– 1
– 2
– 2
– 3
– 3
4
7)
– 4
– 4
3
8)
– 5
– 5
5
2
1
– 5– 4– 3– 2– 1
– 1
– 2
– 3
– 4
– 5
– 6
1
2
3
4
5
x
Equations:
7)
9)
8)
10)
9)
10)
1
2
3
4
5
6
x
Writing equations A
Gradient
(x1,y1)
(x2,y2)
Theta
p134 Ex 16.7
rise y1  y2
Grad 

run x1  x2
General equation: Gradient = Gradient
y  y1
Grad 
m
x  x1
y  y 1  mx  x 1 
Find the equation given a point (x1,y1) and the gradient
1) Find the equation of the line passing through (3,5) with gradient of 2
2) Find the equation of the line passing through (-3,2) with gradient of 
2
3
Writing equations B
rise y1  y2
Grad 

run x1  x2
y  y1
Grad 
m
x  x1
Theta
p135 Ex 16.8
y  y 1  mx  x 1 
Find the equation given two points (x1,y1) and (x2,y2)
1) Find the equation of the line passing through (3,1) and (7,3)
2) Find the equation of the line passing through (-3,2) and (4,-3)