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Question: Find the linear system, which matches the graph.



A ) 2y - x = 6, 2y = 3x - 2
B ) 2y - x = 6, 2y = -3x + 2
C ) 2y + x = 6, 2y = 3x - 2
D ) 2y + x = 6, 2y = 3x + 2

Steps to derive

1 From the graph the y-intercept of line A is 3 and it passes through the points (0, 3) and (2, 2).

2 So, slope of the line A = (2-3)(2-0) = -12
 [Slope = change in y-coordinates / change in x coordinates.]

3 The equation of the line A is y = - 12 x + 3
 [Substitute slope and y-intercept of the line A in the equation y = mx + b]

 [Simplify.]
4 2y + x = 6

5 From the graph the y-intercept of line B is -1 and passing through the points (0, -1) and (2, 2).

6 So, slope of the line B is 2-(-1)2-0 = 32
 [Slope = change in y coordinates / change in x coordinates.]

7 The equation of the line B is y = 32 x - 1
 [Substitute slope and y-intercept of the line B in the equation y = mx + b]

 [Simplify.]
8 2y = 3x - 2

9 The linear system is 2y + x = 6, 2y = 3x - 2



Hence the right answer is Option C

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