4 [Figure 1 and Figure 2, printed on the insert, are provided for use in this question.]
The variables \(x\) and \(y\) are related by an equation of the form
$$y = a x + \frac { b } { x + 2 }$$
where \(a\) and \(b\) are constants.
- The variables \(X\) and \(Y\) are defined by \(X = x ( x + 2 ) , Y = y ( x + 2 )\).
Show that \(Y = a X + b\).
- The following approximate values of \(x\) and \(y\) have been found:
| \(x\) | 1 | 2 | 3 | 4 |
| \(y\) | 0.40 | 1.43 | 2.40 | 3.35 |
- Complete the table in Figure 1, showing values of \(X\) and \(Y\).
- Draw on Figure 2 a linear graph relating \(X\) and \(Y\).
- Estimate the values of \(a\) and \(b\).