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When Igy^2 is plotted against x, a straight line is obtained passing through the points (5, 12) (3, 20). Find y in terms of x giving your answer in the form y = 10^ax + b, where a and b are integers.

a) y = 10^(-2)x + 8

b) y = 10^(2)x - 8

c) y = 10^(2)x + 8

d) y = 10^(-2)x - 8

User ChAmi
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1 Answer

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Final Answer:

The expression for y in terms of x, based on the given points (5, 12) and (3, 20), is y = 10^(-2)x + 8 (Option A).

Step-by-step explanation:

To find the equation in the form y = 10^ax + b, we need to determine the values of a and b. The given points (5, 12) and (3, 20) lie on the curve, so substituting these coordinates into the equation will provide two simultaneous equations. Using the point (5, 12), we get 12 = 10^(-2) * 5 + b, which simplifies to b = 8. Substituting the values of a and b into the general form, we get y = 10^(-2)x + 8.

This result indicates that the relationship between x and y is a power function with a base of 10 raised to the power of -2. The constant term b is found to be 8. Thus, the correct expression is y = 10^(-2)x + 8, corresponding to Option A.

The process involves solving a system of linear equations formed by substituting the given points into the equation. By finding the values of a and b, we can express the relationship between x and y in the desired form. The correct option, y = 10^(-2)x + 8, accurately represents the relationship described by the given data points

User Franchesco
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