Question

Find the point where the graph of the linear equation \[2x-y=4\] cuts the \[x-\text{axis}\].
(a) \[\left( 2,0 \right)\]
(b) \[\left( -2,0 \right)\]
(c) \[\left( 0,-4 \right)\]
(d) \[\left( 0,4 \right)\]

Answer 1

Hint: In this question, in order to determine the point where the graph of the linear equation \[2x-y=4\] cuts the\[x-\text{axis}\], we have to find the \[x-\text{intercept}\]. For that we will have to find the value of \[x\] by putting \[y=0\] in the given linear equation \[2x-y=4\]. Suppose the value of \[x\] is equal to say \[a\] then the point \[(a,0)\] is the required point at which the graph of the equation \[2x-y=4\] cuts the x-axis.

Complete step-by-step solution:
The linear equation is given by \[2x-y=4\].
In order to find the point where the graph of the give linear equation cuts the \[x-\text{axis}\], we will first try to plot the graph of \[2x-y=4\].
The graph of the linear equation is given by

Now in order to find the point where the graph of the linear equation \[2x-y=4\] cuts the x-axis, we have to find the \[x-\text{intercept}\].
 For that we have to find the value of \[x\] by putting \[y=0\] in the given linear equation \[2x-y=4\].
Now by substituting the value \[y=0\] in the linear equation \[2x-y=4\], we get
  $ 2x-y=4 $
 $ \Rightarrow 2x-0=4 $
$ \Rightarrow 2x=4 $
$ \Rightarrow x=\dfrac{4}{2} $
$ \Rightarrow x=2 $
Thus, we get that the \[x-\text{intercept}\] of the linear equation \[2x-y=4\] is given by the point \[\left( 2,0 \right)\].
Hence the graph of the linear equation \[2x-y=4\] cuts the \[x-\text{axis}\] at the point \[\left( 2,0 \right)\].
Therefore option (a) is correct.

Note: In this problem, since we have to find the point at which linear equation \[2x-y=4\] cuts the x-axis. thus the \[y\] coordinate will always be zero. Do not make a mistake by taking the \[x\] coordinate as zero otherwise the point will be on \[y-\text{axis}\] and this will in term give the \[y-\text{intercept}\] of the given linear equation.