Look at the table:

Question

X y
5 -14
6 -16
7 -18
8 -20
9 -22

Write a linear function (y = mx + b) or an exponential function (y = a(b)^x) that models the data.

y = blank

Answer 1

To determine whether the given data can be modeled by a linear or exponential function, let's plot the points on a graph.

The graph of the points will help us determine visually whether the relationship is more linear or exponential.

X | y
5 | -14
6 | -16
7 | -18
8 | -20
9 | -22

Here is the graph of the points:

```
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o |_________
5 6 7 8 9

```

Based on the plotted points, it seems that the relationship between X and y is linear. The points fall along a straight line.

To determine the linear function that models the data, we need to find the slope (m) and the y-intercept (b). We can use any two points from the table to find these values.

Using the points (5, -14) and (9, -22):

m = (y2 - y1) / (x2 - x1)
= (-22 - (-14)) / (9 - 5)
= (-22 + 14) / (9 - 5)
= -8 / 4
= -2

Now that we have the slope (m), we can substitute it into the general form of a linear function y = mx + b and any of the given points to find the y-intercept (b).

Using the point (5, -14):

-14 = -2(5) + b
-14 = -10 + b
b = -14 + 10
b = -4

Therefore, the linear function that models the given data is:

y = -2x - 4