3. The graph of y = 2x + 4 is a straight line which intersects the x - axi at exactly one point, namely (D) (- 2, - 4) (B) (0, - 2) (C) (0, 4) (A) (- 2, 0)
Answers
Answer:
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Step-by-step explanation:
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.
Medium
Solution
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Given y−2x=4⇒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=8−2×2=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=2−2×4=2−8=−6
=RHS, So (4, 2) is not a solution.
