Question

Do the point $\mathrm{P}\left(\frac{3}{2},5\right)$ lie on the line x + y$=\frac{13}{2}$? If so, draw the graph and check it.

Answer 1

We can check whether the point $\left(\frac{3}{2},5\right)$ lies on the line or not by putting the value of the x and y coordinates in the given equation.
$$\begin{gathered} x+y=\frac{13}{2} \\ \mathrm{LHS}=x+y \\ =\frac{3}{2}+5 \\ =\frac{13}{2} \\ \mathrm{So},\mathrm{LHS}=\mathrm{RHS} \\ \mathrm{Since},\text{the values}\mathrm{satisfy}\mathrm{the}\mathrm{equation},\text{the point}\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{graph}\mathrm{of}x+y=\frac{13}{2}. \end{gathered}$$

x+y = $\frac{13}{2}$
The table with the values of x and y satisfying the given equation is shown below:

x	0	6.5
y	6.5	0

The graph of the given equation is as shown:



We can verify it by following the following steps:

(i) Find the value of y for x = 1.5.
(ii) From point P, draw a line parallel to X-axis intersecting the line at Q.
(iii) From point Q, draw a perpendicular to X -axis (i.e. point R).
So, the value of y is 5.
Hence, it is verified.