Question

III. PRE-LAB QUESTIONS - Experiment 8 1. a) Complete the table below. y X 1/x y/x x y 2 2 1/ 2 1 4 1/ 1 0. 58 TL 0.25 16 | b) On graph paper plot y vs. x (appropriately labeling all axes as well as graphing the best fitting line/curve to the data points). c) Is the relationship between the y and x data pairs linear or non-linear? d) Is the relationship between the y and x data pairs direct or inverse? e) Which expression of k (ky/x or k=xy) corresponds to the relationship that you describe in parts c and d? (i.e. the expression where k is a constant) 2. a) Plot y vs. 1/x for the data in question 1. b) Is the relationship linear or non-linear? c) Is the relationship direct or inverse? 3. a) Complete the table below. y/x xºy y 24 4 8 8 16 32 b) On graph paper plot y vs. x (appropriately labeling all axes as well as graphing the best fitting line/curve to the data points) c) Is the relationship between they and x data pairs linear or non-linear? d) Is the relationship between the y and x data pairs direct or inverse? e) Which expression of k (ky/x or k xy) corresponds to the relationship that you describe in parts c and d? (i.e. the expression where k is a constant)

Answer 1

AS PER CHEGG GUIDELINES, I HAVE ANSWERED THE FIRST QUESTION ONLY AS NO SPECIFIC QUESTION WAS ASKED TO SOLVE.

1. a) The complete table is given below -

y	x	1/x	y/x	x.y
2	2	0.5	1	4
1	4	0.25	0.25	4
0.5	8	0.125	0.0625	4
0.25	16	0.0625	0.015625	4

b) The graph of y vs x is given as -

16, 0.25 0 2 4 6 8 10 12 14 16 18

The solid line gives the actual plot while the dotted line gives the best fitted line.

c) If the relation between y and x was linear, the graph of y vs x would be a straight line. As it is not the case, the relationship between y and x is non-linear.

d) Direct relationship between y and x data pairs indicate that as x increases, y increases.

Inverse relationship between y and x data pairs indicate that as x increases, y decreases.

We can see from the table that as x increases, y decreases. So y and x follow inverse relationship.

e) From (c) and (d), we can see that the relationship between y and x is non-linear and inverse.

i.e.

xoh

So we can right $y=\frac{k}{x}$

where k is the constant of proportionality. As the name suggests, it is a constant value.

so  

fic= y

This is the required relation.

This can be seen easily from the 5th column of the table.

[If the values of 4th column would have been constant, then it would have been k = y/x. In that case, y and x would have linear and direct relationship.]