Question

Look at this table:
x y
–
8 74
–
7 65
–
6 56
–
5 47
–
4 38
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=

Answer 1

To determine whether a linear or exponential function best models the data, we need to examine the relationship between the x and y values.

Looking at the x values, we notice that they are decreasing by 1 each time: -8, -7, -6, -5, -4. This suggests a linear relationship as the x values are changing at a constant rate.

Next, we examine the y values. From -8 to -7, the y values decrease by 9 (from 74 to 65). From -7 to -6, the y values also decrease by 9 (from 65 to 56).

Considering the constant rate of change in the y values, we can conclude that a linear function best models the data.

Now, let's determine the values of m and b in the linear equation y = mx + b.

Using the first two data points (-8, 74) and (-7, 65):
m = (65 - 74) / (-7 - (-8)) = -9 / 1 = -9
Using the point (-8, 74) and the slope we just found, we can solve for b:
74 = -9(-8) + b
74 = 72 + b
b = 74 - 72
b = 2

Therefore, the linear function that models the data is:
y = -9x + 2