For each of the graphs given in the figure,select the equation whose graph it is from the choices given below:
$(a)$ For Fig. $(i)$,
$(i)$ $x+y=0$ (ii) $y=2x$ (iii) $y=x$ (iv) $y=2x+1$
$(b)$ For Fig. (ii),
$(i)$ $x+y=0$ (ii) $y=2x$ (iii) $y=2x+4$ (iv) $y=x-4$
$(c)$ For Fig. (iii),
$(i)$ $x+y=0$ (ii) $y=2x$ (iii) $y=2x+1$ (iv) $y=2x-4$

(A-(II), B-(III), C-(IV)) In Fig. $(i)$,the points on the line are $(-1, -2)$,$(0, 0)$,$(1, 2)$. By inspection,$y = 2x$ is the equation corresponding to this graph. You can find that the $y$-coordinate in each case is double that of the $x$-coordinate.
$(b)$ In Fig. (ii),the points on the line are $(-2, 0)$,$(0, 4)$,$(1, 6)$. You know that the coordinates of the points of the graph (line) satisfy the equation $y = 2x + 4$. So,$y = 2x + 4$ is the equation corresponding to the graph in Fig. (ii).
$(c)$ In Fig. (iii),the points on the line are $(-1, -6)$,$(0, -4)$,$(1, -2)$,$(2, 0)$. By inspection,you can see that $y = 2x - 4$ is the equation corresponding to the given graph (line).