Question: Which of the following linear systems matches with the graph?
A ) y = x - 2, 4y = x + 12
B ) y = -x - 2, 4y = x - 12
C ) y = -x + 2, 4y = x - 12
D ) y = x + 2, 4y = x - 12
Steps to derive
1 To find the equation of a line, the y-intercept and the slope of the line are needed.
2 From the graph the y-intercept of line A is 2 and the line is passing through the points (2,0) and (0,2).
3 So, the slope of line A = (2-0)(0-2) = -1
[Slope = difference between y-coordinates / difference between x-coordinates]
4 The equation of the line A is y = -x + 2.
[Substitute slope and y-intercept of line A in the equation y = mx + b]
5 From the graph, line B is passing through the points (4,-2) and (0,-3) and the y-intercept of line B is -3.
6 Slope of line B = -3-(-2)0-4 = 14
[Slope = difference between y-coordintes / difference between x-coordinates]
7 The equation of the line B is y = 14x - 3 .
[Substitute slope and y-intercept of the line B in the equation y = mx + b]
[Simplify.]
8 4y = x - 12
9 The linear system is y = -x + 2, 4y = x - 12.
Hence the right answer is Option C
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