The following gives experimental values of two variables $x$ and $y$ which are known to be connected by a relation of the form $xy=a+bx$.
So, this information was given in a table.
$x=0.4,y=22.0$
$x=0.6,y=15.3$
$x=0.8,y=12.0$
$x=1.0,y=10.0$
$x=1.2,y=8.7$
Plot a graph of $y$ against $\frac{1}{x}$ ad use it to estimate the value of $a$ and $b$.
I did plot a graph, but I did not a straight line, but still tried to make a line of best fit. I couldn't understand then how to make lines for findind the gradient!
Can someone please help me drawing the graph and finding the gradient?
Here is how you do it. Create a new data set as follows. For each data point $(x,y)$, create a new data point $(\frac{1}{x},y)$. Here are the transformed data:
$$\{(2.5, 22.), (1.66667, 15.3), (1.25, 12.), (1., 10.), (0.833333, 8.7)\}$$
Plot these data and you should find a straight line:
The equation of this graph is $y = 7.984X + 2.023$. Since the new $X$ variable is $\frac{1}{x}$, this says $y = 7.984\frac{1}{x} + 2.023$. Multiply through by $x$ and you find $$xy = 7.984 + 2.023x\,.$$ Thus $a \approx 7.984$ and $b \approx 2.023$.
(Are these real measurements? The linear fit is unrealistically good.)