Question

If a line passes through the intersection point of the graphs of the lines x+2y=7 and xâˆ’y=4 and the origin, then find the equation of the line.

A
y=0.5x
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B
y=5x
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C
y=0.2x
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D
y=2x
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Solution

The correct option is C y=0.2xGiven lines are x+2y=7 ......... (1) and x−y=4 ........ (2)To find the point of intersection, we need to solve the equations simultaneously.from eq(2) we get x = y + 4substitute the value of x in the eq(1) we get the value of y and then we can get the value of x from any equation, soBy solving the equations (1) and (2) we getx=5 and y=1.So, the point of intersection is (5,1)Equation of line passing through (5,1) and (0,0) will bey−y1x−x1=y2−y1x2−x1⟹ y−1x−5=−1−5⟹ 5y−5=x−5∴ y=0.2x is the required equation of the line.

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