Question

In the election 60% of voters cast their votes. From an equation and draw the graph for this data. Find the following from the graph.
(1) The total number of voters, if 1200 voters cast their votes.
(2) The number of votes cast, if the total number of voters is 800.

Answer 1

Hint: In this question, firstly we let the number of voters be Y and number of voters who cast their votes be X. Then we form an equation using the given relation which gives an equation of the form Y= mX. We draw the graph and then calculate the required values from the graph.

Complete step-by-step answer:
Let the total number of voters be y.
Let the number of people who cast their vote to be X.
In the question, it is given that:
 60% voters cast their votes. So, we will now find the relation between the number of voters and voters who cast their votes.
Voters who cast their votes = 60% of Y
$ \Rightarrow $X = \[\dfrac{{60}}{{100}}\] Y (1)
$ \Rightarrow $ Y = $\dfrac{5}{3}$X (2)
The plot for the above equation is shown below:

 (1) Given number of voters who cast their votes is 1200 i.e. X=1200
Put the value of x in equation 2, we get;
Y = $\dfrac{5}{3}$$ \times $ 1200=2000
So, the total number of voters is 2000.
(2) Given number of voters = 800 i.e. y= 800.
To calculate the number of total number vote casts, we will again use equation 1:
X = \[\dfrac{{60}}{{100}}\] $ \times $ 800=480
So, the number of votes cast is 480.

Note:
Standard equation of the straight line is y=mx+c ; where x and y is axis, c is constant term and m is slope i.e. angle made between line and x-axis, also we that m=$\tan \theta $. Equation Y = $\dfrac{5}{3}$ x equate with equation y=mx+c; we get c=0 and m =$\dfrac{5}{3}$,$\tan \theta $=$\dfrac{5}{3}$ we know that $\tan {59^0}$= $\dfrac{5}{3}$, so $\theta $=${59^0}$that means angle between line and x-axis is ${37^0}$.