Many ways problem

## Problem

1. Here is a graph showing a straight line. It is not drawn accurately.

The points $(2,3)$ and $(8,8)$ lie on the line.

Another point, $(4,a)$, also lies on the line. Can you work out the value of $a$?

How many different ways can you find to do this?

2. This time, the $x$-coordinate of one of the points is missing—can you work it out?

Did all of your approaches from question 1 work, or did some not? Or perhaps they worked with some modification?

Can you find any new ways to do this question which are different from your methods for question 1?

• The point $(7.3, c)$ lies on the straight line joining $(4.1, 37)$ and $(8.9, 63)$. Find $c$.
• The point $(d, 47.5)$ lies on the straight line joining $(15.05, 42)$ and $(17.55, 56)$. Find $d$.
• The point $(12, e)$ lies on the straight line joining $(8, 20)$ and $(17, 1)$. Find $e$.