Look at this table:
x y
1
–
6.25
2
–
14.11
3
–
21.97
4
–
29.83
5
–
37.69
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine which type of function best models the data, we can examine the relationship between the x- and y-values. In a linear function, the y-values would increase or decrease at a constant rate with each increase in x. In an exponential function, the y-values would increase or decrease at an increasing rate with each increase in x.
Looking at the data, it can be observed that the y-values are increasing at a approximately constant rate with each increase in x. Therefore, a linear function would be the best fit for this data.
To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
We can find the slope using the formula:
m = (change in y) / (change in x)
Using the first two points (1, -6.25) and (2, -14.11), we can calculate the slope:
m = (-14.11 - (-6.25)) / (2 - 1)
m = -14.11 + 6.25
m = -20.36
To find the y-intercept (b), we can substitute one of the given points into the equation y = mx + b and solve for b. Let's use the point (1, -6.25):
-6.25 = -20.36(1) + b
-6.25 = -20.36 + b
b = -6.25 + 20.36
b = 14.11
Therefore, the linear function that models the data is:
y = -20.36x + 14.11