Question

Does the point M (2, 4) lie on the graph of x + y = 6? Verify your answer by drawing the graph.

Answer 1

We can check whether the point lies on the line or not by putting the value of the x and y coordinates in the given equation.
$$\begin{gathered} x+y=6 \\ \mathrm{LHS}=x+y \\ =2+4 \\ =6 \\ \mathrm{So},\mathrm{LHS}=\mathrm{RHS} \\ \mathrm{Since}\text{the values of x and y coordinates}\mathrm{satisf}\text{y}\mathrm{the}\mathrm{equation},\text{the point}\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{graph}\mathrm{of}x+y=6. \end{gathered}$$

x+y = 6
The table with the values of x and y satisfying the given equation is shown below:

x	0	6
y	6	0

The graph of the given equation is as shown :



We can verify it by the following steps:

(i) Find the value of y for x = 2.
(i) From point P, draw a line parallel to X-axis intersecting the line at Q.
(ii) From point Q draw a perpendicular to X -axis (i.e. point R).
So, the value of y is 4.
Hence, it is verified.