5 32
6 38
7 44
8 50
9 56
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
In order to determine if the data can be modeled by a linear or exponential function, we need to examine the relationship between the x-values and the corresponding y-values.
Upon observing the data, we can see that the x-values are increasing by 1 each time, while the y-values are increasing by 6 each time. This indicates a linear relationship, where the slope (m) is constant.
To find the slope, we can choose any two points (x₁, y₁) and (x₂, y₂) from the data. Let's use the points (5, 32) and (6, 38) to find the slope:
m = (y₂ - y₁) / (x₂ - x₁)
m = (38 - 32) / (6 - 5)
m = 6
Now that we have the slope (m), we can find the y-intercept (b) by substituting the values of any point (x, y) from the data into the equation y = mx + b. Let's use the point (5, 32):
32 = 6*5 + b
32 = 30 + b
b = 32 - 30
b = 2
Therefore, the linear function that models the given data is:
y = 6x + 2