Question

Draw the graph for the linear equation given below:
          \[2x-7=0\]
           Which of the following points lie on this line?
A.(3.5,0)
B.(3,0
C.(-2,2)
D.(3.5,2)

Answer 1

Hint: We will simplify the equation to plot the graph and check if the points given to us lie on the plotted graph.

Complete step by step solution:

The equation given to us is \[2x-7=0\]. Which can be rearranged to be written as \[x=\dfrac{7}{2}=3.5\].

Therefore, in the linear equation \[x=3.5\], there is no term for y. This means that y can take any value. If we take reference from the graph we will notice that the line given to us is a straight line which passes from \[x=3.5\] without any slope or a point given by \[y\]. Moreover the line \[x=3.5\] is parallel to \[y-axis\]. Thus the value of \[y\] can be anything from \[0\text{ to }+\infty \text{ and }0\text{ to }-\infty \]
Points lying on the line x=3.5 can be (3.5,0),(3.5,1) or (3.5,−5), etc. but the value of \[x\] should always be \[x=3.5\].
Note that 3.5 lies midway between the points 3 and 4.
Plotting these points on the graph paper and joining them, we get the graph for x=3.5.
From the graph we can verify that the points given to us from the question only points \[A(3.5,0)\,\text{and D}(3.5,2)\] contain the value of \[x\text{ as }x=3.5\]. And the points \[B(3,0)\text{ and }C(-2,2)\] are not lying on the line drawn by us which is \[\begin{align}
  & x=3.5\text{ or }2x-7=0 \\
 & y \\
\end{align}\] .
Therefore , the correct answers for this question will be option (A)(3.5,0) and (D)(3.5,2).



Note : knowing the type of equation and drawing a correct graph is necessary. What is the style of graph is also essential. Here the graph was a straight line with \[x\] having a constant value of \[x=3.5\]. Thus giving the value of \[y\] as anything between \[0\text{ to }+\infty \text{ and }0\text{ to }-\infty \].