Question

Draw the graph to convert miles to kilometres, given 1 mile = 1.6km. Use the graph to find:
(a) How many kilometres are approximately equal to 4.5 miles?
(b) How many miles are approximately equal to 8 km?

Answer 1

Hint: The question is based on the concept of proportionality. Let the length is km be x km and the length corresponding to l in miles be y miles. Now use the constant of proportionality to remove the proportional sign and the statement that 1mile=1.6 miles to get the value of constant of proportionality and hence, the equation of line. Plot the line and search for the points asked in the question to get the answers.

Complete step-by-step answer:
To start with the question, we let the length is km be x km and the length corresponding to l in miles be y miles.
Let us first try to interpret the question in mathematical terms. We know that the length in miles is directly proportional to length in km.
 $ \text{length in mile}\propto \text{length in km}\text{.} $
 $ y\propto \text{x} $
Now according to the definition of proportionality, we can represent the above statement as:
 $ y=mx $
In the above equation, m is the constant of proportionality.
Now according to the question 1mile = 1.6 km. Representing it mathematically using the above equation, we get
 $ y=mx $
 $ \Rightarrow 1=1.6m $
 $ \Rightarrow m=\dfrac{1}{1.6}=\dfrac{5}{8}.............(i) $
Therefore, the value of the constant of proportionality is $ \dfrac{5}{8} $ .
So, the equation after putting m comes out to be:
 $ y=\dfrac{5}{8}x $
Which is a line passing through the origin and slope $ \dfrac{5}{8} $ . So, let us plot it on graph along with the points with y-coordinate 4.5, i.e., 4.5 miles as asked in subpart (a) and point corresponding to 8 km as asked in subpart (b).

As the y-coordinate of each point is in miles and the x-coordinate is the km value corresponding to the measure of the y-coordinate.
So, let us move to the subparts. First we are asked the km conversion of 4.5 miles, which is clear from point A that 4.5miles=7.2km.
Moving to subpart (b), the y-coordinate corresponding to 8km is 5, so, we can say that $ 8km=5miles. $

Note: If you want you can directly calculate the converted values of 4.5 miles and 8km using the equation $ y=\dfrac{5}{8}x $ , but as in the question graph was asked, so we took the graphical approach. But it is a very reliable method and the answers we get through equations are very accurate so, always cross-check your answers using equations.