Question

Kilometres

5 miles = 8 kilometres

The graph showing the relationship between miles and kilometres is a straight line.

a) When plotted on the axes below, the points (0, m) and (5, n) are on this line. Work out the values of m
and n.

b) Use your answer to part a) to plot this line.

40-
35

30

25

20

15

10

5

0

5

10
Miles

15

20

Answer 1

The equation representing the relationship between miles (x) and kilometers (y) is
`\(y = (8)/(5)x\)`, derived from the points (0, 0) and (5, 8).

Let's break down the given information and the steps to find the equation of the line.

a) Establishing the Relationship:

We are given that 5 miles is equal to 8 kilometers, which can be represented as the point (x, y) = (5, 8). Here, x represents the number of miles, and y represents the corresponding number of kilometers.

So, we have the coordinates:

(x, y) = (5, 8)

The points (0, m) and (5, n) are used, and we are told that n = 8 and
m = 0 .

b) Determining the Equation of the Line:

Using the points (0, 0) and (5, 8), we can calculate the slope ( m ) as the change in y divided by the change in x :

`\[ m = \frac{\text{change in } y}{\text{change in } x} = (8 - 0)/(5 - 0) = (8)/(5) \]`

Now, we can use the slope-intercept form of a line ( y = mx + b ), where m is the slope and b is the y-intercept.

Substitute the slope
`(\( m = (8)/(5) \))` and one of the points (let's use (0, 0) into the equation:

`\[ 0 = (8)/(5)(0) + b \]`

Simplify to solve for b :

b = 0

Therefore, the equation of the line is
`\( y = (8)/(5)x \)`.

In summary, the relationship between miles and kilometers is represented by the equation
`\( y = (8)/(5)x \)`, where x is the number of miles and y is the corresponding number of kilometers.