CHAPTER 2: LINEAR LAW

1) Plot a graf v against t. Hence, draw the line of the best fit.t (s) 1 2 3 4 5

v ( ) 4.2 8.3 12.6 16.8 20.9

2) Based on the lines of the best fit in the following graphs, find(i) find the gradient, m(ii) find the y-intercept, c(iii) form the equation for the line of best fit.

(a) (b)

(c) (d)

3) Based on the graphs with lines of best fit, determine the values required.

(i) y when x = 4.4(ii) x when y = 24

(i) q when p = 0.23(ii) p when q = 15

4) In each of the following, plot the graph y against x and draw the line of best fit. Hence, find the values required in each case.

(a)

Scale for x-axis 2 cm : 0.2 unitScale for y-axis 2 cm : 2 unitsFrom your graph, determine the value of

(i) y when x = 0.3(ii) x when x = 10.2(ii) x when y = 3.8

(b)

Scale for x-axis and y-axis 2 cm : 5 unitsFrom your graph, determine the value of

(i) y when x = 7.5(ii) y when x = 27(ii) x when y = 18

5) In each of the following, plot the graph of y against x and draw the line of the best fit. From the graph:

(i) find the equation for the line of best fit(ii) find the values required

(a)

- Find the value of y when x =1.8- Find the value of x when y = 24.5

(b)

- Find the value of y when x =9- Find the value of x when y = 26

(c)

- Find the value of y when x =42- Find the value of x when y = 100

x 0.20 0.40 0.60 0.80 1.00 1.20y 2.1 4.2 6.1 8.2 10.4 12.6

x 5 10 15 20 25 30 35y 26 23 20 17 14 11 7.5

x 0.5 1.0 1.5 2.0 2.5 3.0 3.5y 6 9.5 12.5 16 19 22 25.5

x 2 4 6 8 10 12y 36 30 24.8 18.8 13.2 7.6

x 10 20 30 45 60 80y 25 45 65 92 124 162

6) Form an equation for the straight line in each of the following graphs. Hence, find(i) value of y when x =2(ii value of x when y =12

(a) (b)

(c)

(a)

(b)

(c)

(d)

2.2) Application of linear law to non-linear relations(A)1) Convert each of the following of the non-linear equations to linear form . Express Y and X in tems of x and/ or and/ or y. Hence, state the values of m and c.

Equation Linear equation Y X m c

1)

2)

3)

4)

5)

6)

7)

8)

9)

(D) Solve each of the following

1) The table shows the values of x and y obtained from an experiment. The variables x and y are related by the equation , where a and b are constants.

(a) Plot the graph against .(b) Use your graph in (a), find the values of

(i) a (ii) b

2) The table shows the values of x and y are related by the equation , where

p and q are constants.

(a) Plot the graph against . Hence, draw a line of best fit.(b) Use your graph in (a), find the values of

(i) p (ii) q

3) The table shows the values of x and y obtained from an experiment. The variables x and y are related by the equation , where a and b are constants.

(a) Plot the graph against . Hence, draw a line of best fit.(b) Use your graph in (a), find the values of

(i) a (ii) b

x 1.5 2 3 4 5 6y 18 40 141 330 620 1100

x 0.5 1.0 1.5 2.0 2.5 3.0y 29 13.6 8 4.9 2.7 1.1

x 1 2 3 4 5 6y 6.3 8.0 10.3 12.4 16 20