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Question

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(a) \[\left( 2,0 \right)\]

(b) \[\left( -2,0 \right)\]

(c) \[\left( 0,-4 \right)\]

(d) \[\left( 0,4 \right)\]

Answer
Verified

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 \[\left( 2,0 \right)\].