Question 754176
In the xy plane line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t, t+1), what is the value of t?

I don't understand the significance of the line passing through the origin. 

The answer is -4/3
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In the xy plane line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant.
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4x+y = k
y = -4x+k  --> slope = -4
The line perpendicular has a slope of +1/4, the negative inverse.
Use y = mx + b and the point (0,0) to find b
0 = (1/4)*0 + b
b = 0
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The equation of the line is y = (1/4)x or y = x/4
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At point (t,t+1), t+1 = t/4
4t+4 = t
3t = -4
t = -4/3
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The Origin is not significant, it could be any point to find the equation of the line.