Simplifying expressions
y . y . y . y . x
xy4
a - 5c, when a = 7 and b = -3
= 7 - (5 . -3)
= 7 - (-15)
= 7 + 15
= 22
5x + 15 = 60
5x = 60 - 15
5x = 45
x = 9
Look at the set of coordinates below:
x: 1 , 2 , 3 , 4 , 5 , 6
y: 4 , 7 , 10 , 13 , 16 , 19
Find the rule that generates this pattern?
y = 3x + 1
x6 . x2
x8
2m . 2m . 2m
8m3
x + 8 - y, when x = 5 and y = 9
= 5 + 8 - 9
= 13 - 9
= 4
13x + 12 = -1
13x = -1 - 12
13x = -13
x = -1
Look at the set of coordinates below:
x: 1 , 2 , 3 , 4 , 5 , 6
y: 3 , 9 , 15 , 21 , 27 , 33
Find the rule that generates this pattern?
y = 6x - 3
a-4
1 / a4
2x2y . 3y2
6x2y3
2(a - b - c), when a = 3, b = - 6 and c = 9
= 2(3 - (-6) - 9)
= 2(3 + 6 - 9)
= 2(0)
= 0
15 - 8x = 135
-8x = 135 - 15
-8x = 120
x = -15
Look at the set of coordinates below:
x: 1 , 2 , 3 , 4 , 5 , 6
y: -6 , -10 , -14 , -18 , -22 , -26
Find the rule that generates this pattern?
y = -4x - 2
(3a4)2
9a8
4p2q . 5p3q
20p5q2
3(x + y)2, when x = 6 and y = 8
= 3(6 + 8)2
= 3(14)2
= 3(196)
= 588
Three times James' age minus nineteen is 41. What is James' age?
3x - 19 = 41
3x = 41 + 19
3x = 60
x = 20
Look at the set of coordinates below:
x: 1 , 2 , 3 , 4 , 5 , 6
y: 10.5 , 15 , 19.5 , 24 , 28.5 , 33
Find the rule that generates this pattern?
y = 4.5x + 6
3(2x4)4
= 3 . 16x16
= 48x16
2k2m . 3km . 5mk
30k4m3
4(x - 5)2 - y, when x = 2 and y =-2
= 4(2 - 5)2 - (-2)
= 4(-3)2 + 2
= 4(9) + 2
= 36 + 2
= 38
A tyre company has a discounted set of four tyres by $95 to give a sales price of $645. How much is the originial price of a single tyre?
4x - 95 = 645
4x = 645 + 95
4x = 740
x = $185
y = mx + c is a linear equation, explain why?
When graphed, it forms a straight line, and the highest power of the variable x is 1.
This form also reveals that the relationship between x and y is constant and predictable, with a constant slope (m) and y-intercept (c).
2(3x2y3)4
= 2 . 81x8y12
= 162x8y12