Question

Draw the graph of the equation y - 2x = 4 and then answer the following.
(i) Does the point (2, 8) lie on the line? Is (2, 8) a solution of the equation? Check by substituting (2, 8) in the equation.
(ii) Does the point (4, 2) lie on the line? Is (4, 2) a solution of the equation? Check algebraically also.

Answer 1

Given $y-2x=4\Rightarrow y=2x+4$
Table of Solutions

x	y = 2x + 4	(x, y)	Point
0	y = 2(0) + 4 = 4	(0, 4)	A(0, 4)
2	y = 2(-2) + 4 = 0	(-2, 0)	B(-2, 0)
1	y = 2(1) + 4 = 6	(1, 6)	C(1, 6)

Plotting the points A, B and C on the graph paper and joint them to get the straight line BC as shown in graph sheet. This line is the required graph of the equation y - 2x = 4.
(i) Plot the point (2, 8) on the graph paper. From the graph it is clear that the point (2, 8) lies on the line.
Checking algebraically: On substituting (2, 8) in the given equation, we get
LHS $y-2x=8-2\times 2=8-4=4$ RHS, So (2, 8) is a solution
(ii) Plot the point (4, 2) on the graph paper. You fin that (4, 2) does not lie on the line.
Checking algebraically: By substituting (4, 2) in the given equation we have
LHS $=y-2x=2-2\times 4=2-8=-6\ne RHS$, So (4, 2) is not a solution.