Problem

b: $y$-intercept or starting \begin{tabular}{|c|c|} \hline$X$ & $Y$ \\ \hline 0 & 3 \\ \hline 1 & 7 \\ \hline 2 & 11 \\ \hline 3 & 15 \\ \hline \end{tabular} What is the rate? What is the starting value? Write the equation:

Solution

Step 1 :The question is asking for the rate and the starting value of a linear function represented by the given table. The rate of a linear function is the slope, which can be calculated by taking the difference in the y-values divided by the difference in the x-values. The starting value is the y-intercept, which is the y-value when x is 0.

Step 2 :From the table, we can see that the x-values are [0, 1, 2, 3] and the corresponding y-values are [3, 7, 11, 15].

Step 3 :By calculating the difference in the y-values divided by the difference in the x-values, we find that the rate is \(4.0\).

Step 4 :The starting value is the y-value when x is 0, which is \(3\) from the table.

Step 5 :Final Answer: The rate is \(\boxed{4}\) and the starting value is \(\boxed{3}\). The equation of the line is \(y = 4x + 3\).

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Source: https://solvelyapp.com/problems/UM9Pa5C8Lm/

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