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Write an equation in the form r(x) = p(x) / q(x) for each function shown below.Pls see pic for details

Write an equation in the form r(x) = p(x) / q(x) for each function shown below.Pls-example-1
User VarunGupta
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1 Answer

17 votes
17 votes

c.

The line equation is of the form


y=mx+c\ldots(1)

From the graph, we observe and find these points

(1,5) and (0,4) lie on the given line.

Substituting x=1, y=5 in equation (1), we get


5=m(1)+c


m+c=5\ldots\text{.}(2)

Substituting x=0, y=4 in equation (1), we get


4=m(0)+c


c=4

Substituting c=4 in equation (2), we get


m+4=5


m=5-4


m=1

Substituting c=4,m=1 in equation (1), we get


y=x+5

We need to write this equation in the form of r(x) = p(x) / q(x).


r(x)=(p(x))/(q(x))\ldots(3)

Let r(x)=x+5, q(x)=x, and subsitute in the equation , we get


x+5=(p(x))/(x)

Using the cross-product method, we get


x(x+5)=p(x)


x* x+x*5=p(x)


x^2+5x=p(x)

Substitute values in equation (3), we get


x+5=(x^2+5x)/(x)

Hence the required equation is


x+5=(x^2+5x)/(x)

User Lakmi
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