Question

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

Answer 1

Hint: We know that 1 mile is equal to 1.6 kilometres. Let the distance in kilometres be x and the distance in miles be y, then the relation between miles and kilometres will be $1=1.6\times m$ , where m is the slope. Find the value of the slope and substitute it in the line equation when slope and intercept are given, and then using it plot the graph.

Complete step-by-step answer:
We are given to draw a graph to convert miles into kilometres and the value of one mile is equal to 1.6 kilometres.
The line equation when a slope and y-intercept are given is $y=mx+c$ , where m is the slope and c is the y-intercept.
Let the distance in kilometres be x and the distance in miles be y.
Then we can relate miles and kilometres as $y=mx\to 1mile=m\times 1.6km$ , where m is the slope.
Slope is $m={\displaystyle \frac{1}{1.6}}={\displaystyle \frac{10}{16}}={\displaystyle \frac{5}{8}}$
Now, substitute the slope in the line equation where the y-intercept is zero because when the distance is zero miles, the corresponding distance in kilometres is also zero.
 $$\begin{gathered} y=mx+c \\ m={\displaystyle \frac{5}{8}},c=0 \\ \Rightarrow y={\displaystyle \frac{5}{8}}x+0 \\ \Rightarrow y={\displaystyle \frac{5}{8}}x \end{gathered}$$
Now using the line equation $y={\displaystyle \frac{5}{8}}x$ , plot the graph.

When the value of y is 4.5 miles then the corresponding value of x in kilometers is $4.5={\displaystyle \frac{5}{8}}x\to x={\displaystyle \frac{4.5\times 8}{5}}=7.2km$
When the value x is 8 km then the corresponding value of y in miles is $y={\displaystyle \frac{5}{8}}\times 8\to y=5miles$

7.2 kilometres is 4.5 miles and 5 miles is 8 kilometres.

So, the correct answer is “Option C”.

Note: The slope of a line can be obtained by the ratio of change in y-coordinates to the change in x-coordinates. Slope is a constant value but it has units. The units of slope will be the ratio of y-units to the x-units. Here, the units of slope are miles per kilometres. So do not assume that the slope will not have units. Do not confuse graphs with charts as a graph is a type of chart, but not vice-versa. All graphs are charts, but all charts need not be graphs.