Look at this table:
x -10, -9, -8, -7, -6
y 92, 82, 72, 62, 52
Write a linear function (y = mx + b) or an exponential function (y = a(b)^x) that models the data.
To determine if the data follows a linear or exponential pattern, we can calculate the ratios of consecutive y values:
92 / 82 = 1.122
82 / 72 = 1.138
72 / 62 = 1.161
62 / 52 = 1.192
Since the ratios are not consistent, the data does not follow an exponential pattern. Therefore, we will look for a linear model.
We can use the first and last data points (-10, 92) and (-6, 52) to find the equation of the line:
First, calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (52 - 92) / (-6 - (-10))
m = -40 / 4
m = -10
Next, use the slope and one of the points in the equation y = mx + b to solve for the y-intercept (b). Let's use the first point (-10, 92):
92 = -10(-10) + b
92 = 100 + b
b = 92 - 100
b = -8
Therefore, the linear function that models the data is:
y = -10x - 8