Question

For each graph given below, four linear equations are given. Out of these find the equation that represents the given graph.Equations are
A) $y=x$
B) $x+y=0$
C) $y=2x$
D) $2+3y=7x$

Answer 1

From the graph we see (1, -1) (0, 0) (-1, 1) lie on the same line.
So these are the solutions of the required equation i.e. if we substitute these points in the required equation it should be satisfied.

So, we have to find an equation that should be satisfied. So, we have to find an equation that should be satisfied by these pairs.
If we substitute (1, -1) in the first equations y = x is not satisfied. So y = x is not the required equation.

Putting (1, -1) in x + y = 0 we find that it satisfies the equation. In fact all the three points satisfy the second equation. So x + y = 0 is the required equation.

We now check whether y = 2x and 2 + 3y = 7x are also satisfied by (1, -1)and (-1, 1). We find they are not satisfied by even one of the pairs, leave alone all three. So, they are not the required equations.