6.6.3 SPM practice 3 (Linear Law) – Question 3

Question 3
The table below shows the values of two variables, x and y, obtained from an experiment. The variables x and y are related by the equation $\frac{a}{y}=\frac{b}{x}+1$ , where k and p are constants.


(a) Based on the table above, construct a table for the values of $\frac{1}{x}$ and $\frac{1}{y}$ . Plot $\frac{1}{y}$ against $\frac{1}{x}$ , using a scale of  2 cm to 0.1 unit on the $\frac{1}{x}$ – axis and  2 cm to 0.2 unit on the $\frac{1}{y}$ – axis. Hence, draw the line of best fit.
(b) Use the graph from  (b)  to find the value of
(i)  a,
(ii)  b.

Solution
Step 1 : Construct a table consisting X and Y.




Step 2 : Plot a graph of Y against X, using the scale given and draw a line of best fit

Step 3 : Calculate the gradient, m, and the Y-intercept, c, from the graph

Step 4 : Rewrite the original equation given and reduce it to linear form

Step 5 : Compare with the values of m and c obtained, find the values of the unknown required