Answer to Question #24726 in Abstract Algebra for Brandon Phillips

Question

Assume that y varies directly with x. If y = 910 when x =2, y=34 when x =7.

Answer 1

Since y varies directly with x, then their dependence is described by linear function y=kx+b.

Since we have that y = 910 when x =2, y=34 when x =7, then we can substitute these points in our linear function:
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2k+b=910
7k+b=34
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Subtracting first out of second, and dividing by 5, we have that:

k=(34-910)/5=-175.2
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As we have now value of k, from first equality we have:

b=910-2k=910+350.4=1260.4

With obtained coefficients we can describe y as y=(-175.2)x+1260.4