6.6.2 SPM practice 3 (Linear Law) – Question 2

Question 2
The table below shows the corresponding values of two variables, x and y, that are related by the equation $y=5h{x}^{2}+\frac{k}{h}x$ , where h and k are constants.

(a) Using a scale of 2 cm to 1 unit on the x – axis and 2 cm to 0.2 units on the $\frac{y}{x}$ – axis, plot the graph of $\frac{y}{x}$ against x .  Hence, draw the line of best fit.

(b) Use your graph in (a) to find the values of
(i) h,
(ii) k,
(iii) y when x = 6.

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

(b) (iii)
find the value of y when x = 6.