Look at the table:
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
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