Use the table to answer the question.%0D%0A%0D%0Ax%0D%0A%0D%0Ay%0D%0A%0D%0A1%094%0D%0A−3%0D%0A−%0D%0A3%0D%0A8%0D%0AFind the rate of change and the initial value of the linear function given as a table of values.%0D%0A%0D%0A(1 point)%0D%0AThe rate of change is m=%0D%0A%0D%0A=%0D%0A, and the initial value is b=%0D%0A%0D%0A=%0D%0A.

3 answers

To find the rate of change, we can use the formula:

\(\text{{rate of change}} = \frac{{\text{{change in y}}}}{{\text{{change in x}}}}\)

Using the table, we can see that when x changes from 1 to -3, y changes from 4 to 3.

So, the change in y is 3 - 4 = -1, and the change in x is -3 - 1 = -4.

Therefore, the rate of change is:

\(\text{{rate of change}} = \frac{{-1}}{{-4}} = \frac{1}{4}\)

To find the initial value, we can use the formula:

\(\text{{initial value}} = y - \text{{rate of change}} \cdot x\)

Using any of the given values in the table, we can substitute the values and solve for the initial value.

Let's use the first point (1, 4):

\(\text{{initial value}} = 4 - \frac{1}{4} \cdot 1 = 4 - \frac{1}{4} = \frac{15}{4}\)

So, the initial value is:

b = \(\frac{15}{4}\)

Therefore, the rate of change is m = \(\frac{1}{4}\), and the initial value is b = \(\frac{15}{4}\).
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The rate of change is \(m = \frac{1}{4}\), and the initial value is \(b = \frac{15}{4}\).