The equation of line m is 3x + 4y = 12. The line whose equation is 3x + 4y = k is 2 units from m. Find the two possible values of k.
+128474 3x + 4y = 12
The x intercept of this line is ( 0, 3)
Using the formula for the distance from a point to a line we have that
l 3 ( 0) + 4(3) - k l
__________________ = 2
sqrt ( 3^2 + 4^2)
1 3(0) + 4(3) - k l
__________________ = 2 ...... multiply both sides by 5 and simplify
5
l 12 - k l = 10 we have two equations
12 - k = 10 12 - k = -10
k = 2 or k = 22
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