The table below shows experimental values of two variables $x$ and $y$ which are connected by an

Question

The table below shows experimental values of two variables $x$ and $y$ which are connected by an equation of the form $ax^2 + by = 1$, where $a$ and $b$ are constants.

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$y$	$0.47$	$0.87$	$1.53$	$2.47$	$3.87$	$5.14$

Using a suitable scale, plot the graph of $y$ against $x^2$. Use your graph to

determine which value of $y$ is inaccurate and estimate its correct value,
estimate the value of $a$ and of $b$.
By drawing a suitable straight line, find the values of $x$ and $y$ which satisfy the following pair of simultaneous equations.
$ax^2 + by = 1$
$2x^2 + y = 3$

Accepted Answer

(i) The value y=3.87 at x=5 is inaccurate; corrected y≈3.7. (ii) a≈-0.380, b≈2.86. (iii) x≈1.11, y≈0.515.

Linear Law - Plotting Linearised Data and Lines of Best Fit

Linear Law - Plotting Linearised Data and Lines of Best Fit

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