1. Example A spring ( 彈簧 )was loaded with weights (W) in g. The length of the spring (L) is measured for each different load. Load, W (g) 20406080100 Length of Spring, L (cm) 16.020.024.528.031.5 equation Objective : To find an equation to describe the relationship between W (load) and L (length of spring).

2. Graphical Analysis Since we need to find the relationship between W and L, therefore, the name of the graph should be The graph of L against W. L will be the vertical axis and W will be the horizontal axis. On a graph paper, following your steps of plotting graph In mathematics, draw the vertical and horizontal axes and labelled them properly. Then select suitable scale for the two axes.

3. Graphical Analysis The largest number of each scale should cover the maximum data for that axis. In this question, maximum scale should be more than 100 (say 110 or 120) for the load (horizontal), and more than 31.5 (say 32) for the length (vertical). Your scale should be very easily scaled. For example, for each largest division (5 small sub-divisions) should represent 1 or 2, or 5 or 10 or the multiples and NEVER represent 3 or 7.

4. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W /g L /cm (20, 16.0) (40, 20.0) (60, 24.5) (80, 28.0) (100,31.5)

5. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W / g L / cm The y-intercept,c is about _____cm 12.3 The slope,m : 0.195 The equation : y = m x +c 12.3 (96,31) (4,13) In maths, x and y to for the two axes, however, in this example, the two axes are W and L

6. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W/g L L / cm The y-intercept,c is about _____cm 12.3 The slope,m : 0.195 The equation : L L = m x +c So, L replace y

7. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W W/g L L / cm The y-intercept,c is about _____cm 12.3 The slope,m : 0.195 The equation : LW L = m W +c and W replace x

8. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W W/g L L / cm The y-intercept,c is about _____cm 12.3 The slope, m : 0.195 The equation : LW L = m W + c

9. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W W/g L L / cm c The y-intercept,c is about _____cm 12.3 m The slope, m : 0.195 The equation : L 0.195 W c L = 0.195 W +c When W=0, L = c (or 12.3 in this case), so c=12.3

10. The graph of L against W 0 5 10 15 20 25 30 35 020406080100120 W W/g L L / cm c The y-intercept,c is about _____cm 12.3 m The slope, m : 0.195 The equation : L 0.195 W 12.3 L = 0.195 W + 12.3