Write a rule for the linear function in the table SolutionFr

Write a rule for the linear function in the table.

From the table we can observe that f(x) is equal to 5 times x

Hence the linear function is f(x)=5x

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Given points are (0,0), (1,5),(2,10),(3,15)

Let the linear function be f(x)=ax+b

Since it passes through (0,0), so sunstitute x=0 and f(x) in f(x)=ax+b, then b=0

Hence f(x)=ax

The function passes through the point (1,5)

Substitute x=1 and f(x)=5 in f(x)=ax. Then

5=a(1) implies a=5

Hence the linear function is f(x)=5x