Look at this table:
x y
4 39
5 48
6 57
7 66
8 75
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Looking at the values of x and y, we can see that the difference between consecutive y values (y2 - y1) is always the same. Therefore, we can conclude that the data follows a linear pattern.
To find the linear function that models the data, let's calculate the slope (m) and y-intercept (b) using the given data points:
Slope (m) = (y2 - y1) / (x2 - x1)
m = (48 - 39) / (5 - 4) = 9 / 1 = 9
Now that we have the slope, we can plug it into the equation y = mx + b and use any of the given data points to solve for the y-intercept (b). Let's use the first data point (4, 39):
39 = 9(4) + b
39 = 36 + b
b = 39 - 36
b = 3
Therefore, the linear function that models the data is:
y = 9x + 3