Chapter 7: Problem 4

It is known that \(y\) is proportional to \(x\). Experimental measurements are recorded in Table \(7,2 .\) \begin{tabular}{ccccc} \hline\(y\) & 30 & 40 & 50 & 60 \\ \(x\) & 5 & \(6.67\) & \(8.33\) & 10 \\ \hline \end{tabular} (a) Determine the equation connecting \(y\) and \(x\). (b) Calculate \(y\) when \(x=2\).

Short Answer

Expert verified

Answer: The equation connecting y and x is y = 6x, and the value of y when x=2 is y = 12.

Step by step solution

Understanding the relationship between y and x

As given, y is proportional to x. This type of relationship can be expressed as y=kx, where k is the constant of proportionality.

Determine the constant of proportionality, k

We can find the constant of proportionality, k, using the data given in the table. Let's pick the first data point, where y=30 and x=5. Using the equation y=kx, we have: 30 = k(5) Now, isolate k by dividing both sides by 5: k = 30/5 k = 6

Write the equation connecting y and x

Now that we have found the value of the constant of proportionality, k, we can write the equation connecting y and x as follows: y = 6x

Calculate y when x=2

Using the equation y=6x, we will now calculate the value of y when x=2: y = 6(2) y = 12 So when x=2, the value of y is 12. The equation connecting y and x is y = 6x, and the value of y when x=2 is y = 12.

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Short Answer

Step by step solution

Understanding the relationship between y and x

Determine the constant of proportionality, k

Write the equation connecting y and x

Calculate y when x=2

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