Look at this table:
x y
1
–
1
2 5
3 11
4 17
5 23
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the given data can be modeled by a linear function or an exponential function, we need to examine the relationship between the x-values and the corresponding y-values.
Looking at the table, we can observe that as the x-values increase by 1, the y-values increase by a constant amount. This suggests that the data can be modeled by a linear function.
To find the equation of the linear function, we need to determine the slope (m) and the y-intercept (b).
Taking the first and second data points, we can find the slope using the formula:
m = (change in y) / (change in x) = (5 - 1) / (2 - 1) = 4 / 1 = 4
The y-intercept can be determined by substituting one of the points into the equation:
1 = 4(1) + b
1 = 4 + b
b = 1 - 4
b = -3
Therefore, the linear function that models the data is:
y = 4x - 3