1. Name : ___________( ) Class: _______ Date : _______
Term 3 : Unit 3 Linear Law
Name : ___________( ) Class: _______ Date : _______
3.1 Linear Law
3.2 Applications of Linear Law
8. Linear Law
8.1 Linear Law
8.2 Applications of Linear Law 1

2. Linear Law Objectives 3.1 Linear Law
In this lesson, you will learn how to
convert a non-linear relation to linear form,
use new variables X and Y to draw the graph of Y = mX + c,
estimate the values of the gradient m and the Y-intercept, c,
use the values of m and c to estimate unknown constants in the original
equation,
and use the linear graph of Y = mX + c to obtain the estimated values of x and y.
8.1 Linear Law
Objectives
In this lesson you will learn how to convert a non-linear relation to linear form; use new variables X and Y to draw the graph of Y = mX + c, and estimate the values of the gradient m and the Y-intercept c; use the values of m and c to estimate unknown constants in the original equation and use the linear graph of Y = mX + c to obtain the estimated values of x and y.

3. Linear Law Example 1 Two variables x and y are related by the equation
Calculate values of y for some values of x. x X y Y –
0.5 2 7 1 5 4 x y –
0.5 7 1 5 2 4
Example 1, Page 165
Graph of Y against X.
The points lie on a straight line.

4. Linear Law Example 2 Two variables x and y are related by the equation
Calculate values of xy(Y ) for some values of x. x X y Y – –1 1 4 2
0.75 3 9
0.56 5 x Y –1 1 4 3 9 5
Example 2, Page 165
Graph of Y against X.
The points lie on a straight line.

5. The line passes through (1, – 1).
Linear Law
Example 3
Two variables x and y are related such that when
is plotted against , a straight line is obtained.
The line passes through the points A(1, –1) and B(4, 14). Express y in terms of x.
The line passes through (1, – 1).
Example 6, Page 167

6. The points lie on a straight line.
Linear Law
Example 4
Two variables x and y are related by the equation
(b) Draw the graph of lg y against lg x.
Exercise 8.1, Question 3, Page 170
The points lie on a straight line. x
lg x
lg y y
0.1
– 1
–0.80
0.16
0.5
– 0.30
0.25
1.77 1
0.70 5 3
0.48
1.41
26.0

7. Linear Law
Example 5
Two variables x and y are related in such a way that
when xy is plotted against , a straight line is
obtained. The line passes through the points
A(–1, –1) and B(5, 2).
(a) Find an expression for y in terms of x.
Exercise 8.1, Question 6, Page 170
(b) Find the value of y when x = 2.

8. Linear Law Objectives 3.2 Applications of Linear Law
In this lesson, you will apply linear law to analyse experimental data.
8.2 Applications of Linear Law
Objectives
In this lesson you will apply linear law to analyse experimental data.

9. Linear Law
Example 6
The table shows experimental values of two quantities x and y which are
known to be connected by an equation of the form
Plot against and use the graph to estimate the values of a and b. x X y Y
0.50
0.71
1.61
0.62
1.00
0.83
1.20
1.50
1.22
0.61
1.64
2.00
1.41
2.50
1.58
0.42
2.38
3.00
1.73
0.38
2.63 x y
0.50
1.61
1.00
0.83
1.50
0.61
2.00
2.50
0.42
3.00
0.38
Example 9, Pages 172

10. Linear Law
Example 7
The table shows experimental values of the variables x and y.
It is known that x and y are related by the equation y = axn (a, n are constants)
(a) Express the equation in a form to draw a straight line graph. x X y Y 3
0.48 13
1.11 4
0.60 20
1.31 5
0.70 29
1.46 6
0.78 39
1.59 7
0.85 49
1.69 8
0.90 61
1.79 x y 3 13 4 20 5 29 6 39 7 49 8 61
Example 12, Page 176
(b) Draw the graph to estimate n and a.

11. Linear Law (c) Calculate the value of x when y = 66.
Using lg y = 1.62 lg x ,
lg 66 = 1.62 lg x
1.82 = 1.62 lg x
lg x = 0.92
x = 0.82

12. Linear Law
Example 8
The table shows experimental values of the variables x and y.
It is known that x and y are related by the equation y = ax2 + bx (a, b are constants)
(a) Express the equation in a form to draw a straight line graph. x X y Y 1
1.6 2
7.2
3.6 3
16.8
5.6 4
30.4
7.6 x y 1
1.6 2
7.2 3
16.8 4
30.4
Exercise 8.2, Question 6, Page 178
(b) Draw the graph to estimate a and b.