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Question: Which of the following linear systems matches with the linear system in the graph?



A ) 3y = -2, y = 1
B ) 3y = 2x, y = -x - 1
C ) 3y = 2x, y = x - 1
D ) None of the above

Steps to derive

1 The equation of the line in slope-intercept form with slope m and y-intercept b is y = mx + b

2 From the graph y-intercept of line A is 0 and slope is 23.

3 The equation of the line A is y = 23x
 [Substitute slope = 23 and y-intercept = 0 in the slope-intercept form equation.]

4 3y = 2x
 [Simplify.]

5 From the graph the y-intercept of line B is -1 and slope is 1.

6 The equation of the line B is y = x - 1
 [Substitute slope = 1 and y-intercept = -1 in the slope-intercept form equation.]

7 The linear system is
3y = 2x
y = x - 1.



Hence the right answer is Option C

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