Modul Mas

Chapter 2 : Linear Law

Use graph paper to answer this question.

1. The table below shows the values of x and y obtained from an experiment.

x	1	2	3	4	5	6
y	5	40	135	320	625	1080

It is known that x and y are related by the equation y = ax^b+1, where a and b are constants.

plot log₁₀ y against log₁₀ x using a scale 2 cm to 0.1 unit on the log₁₀ x-axis and 2 cm to 0.5 units on the log₁₀ y-axis.based on your graph , estimate the values of a and b.

2. The table below shows the values of x and y obtained from an experiment. Variables x and y are related by the equation y = pk ^x, where p and k are constant.

x	2	4	6	8	10	12
y	3.16	5.50	9.12	16.22	28.84	46.77

plot log₁₀ y against x using a scale 2 cm to 2 unit on the x-axis and 2 cm to 0.2 units on the log₁₀ y-axis. Hence draw the line of best fit. Used your graph from a) , estimate the values of p and k.

3. The table below shows the values of x and y obtained from an experiment. The variables x and y are related by the equation y = px , where p and r are constants.

x	1.0	2.0	3.0	4.0	5.0	5.5
y	5.5	4.7	5.0	6.5	7.7	8.4

Plot xy against x² by using a scale 2 cm to 5 units on both axes. Hence draw the line of best fit

Used your graph from a) , to find the values of p and r

4. The table below shows the values of x and y obtained from an experiment. Variables x and y are related by the equation y = pk ^{x + 1}, where p and k are constants.

x	1	2	3	4	5	6
y	4.0	5.7	8.7	13.2	20.00	28.8

plot log₁₀ y against ( x + 1 ) using a scale 2 cm to 1 unit on the (x + 1)-axis and 2 cm to 0.2 units on the log y-axis. Hence draw the line of best fit

Used your graph from a) , estimate the values of p and k.

5. The table below shows the experimental result of two variables x and y . It is known that x and y are related by the equation y = ax³ - bx, where a and b are constants.

x	1	2	3	4	5
y	-1.5	9	43.5	114	232.5

Change the equation to linear form, hence draw a straight line graph for the values of x and y.

b) From your graph determine the values of a and b find the values of y when x = 3.5

6. The table shows the corresponding values of x and y obtained from an experiment.

x	10	12	15	18	20	22	28
y	3.12	2.99	2.85	2.76	2.71	2.68	2.63

a) Plot y against, using a scale 2 cm to 0.1 unit on y- axis and 2 cm to 0.01 unit on - axis. Hence draw the line of best fit.

Given that x and y are related by the equation , where a and b are constants, Find the values of a and b.

7. The table shows the values of two variables x and y , obtained from an experiment.

x	1	2	3	4	5	6
y	1	1	0.78	0.63	0.52	0.44

It is predicted that x and y are related by the equation where a and b are constants Plot x y against , using a scale 2 cm to 0.4 unit on xy -axis and 2 cm to 0.1 unit on - axis. Hence draw the line of best fit.

b) From the graph in a) Find the values of a and b

8. The table shows the corresponding values of x and y obtained from an experiment.

x	1	2	3	4	5	6
y	0.25	0.5	1	2	4	8

It is known that x and y are related by the equation , where p and q are constants. Plot against x, using a scale 2 cm to 0.3 unit on - axis and 2 cm to 1 unit on x- axis. Hence draw the line of best fit.

b) From the graph in a) , Find the values of p and q.

9. The table shows the corresponding values of x and y obtained from an experiment.

x	1	2	3	4	5	6
y	1.75	3.65	5.57	7.5	9.44	11.4

Plot against , using a scale 2 cm to 0.04 unit on - axis starting from 1.70 and 2 cm to 0.1 unit on - axis. Hence draw the line of best fit.

Given that x and y are related by the equation , where p and q are constants, Find the values of p and q.

10. The table shows the corresponding values of x and y obtained from an experiment. Variables x and y are related by equation

x	0	1	2	3
y	1.414	1.732	2.00	2.236

Plot y² against x, Hence draw the line of best fit.

From an equation relating y to x , Find the values of h and k.