Look at this table:
x y
1
–
4
2 1
3 6
4 11
5 16
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 table can be modeled by a linear function or an exponential function, let's first examine the relationship between the x and y values.
We can observe that for every increase in x by 1, the corresponding y value increases by 5. This indicates a constant rate of change. Therefore, the data can be modeled using a linear function.
Now, to find the slope (m) and y-intercept (b) for the linear function, we can use the formula:
m = (change in y) / (change in x)
Using the values from the table, we can calculate the slope:
m = (16 - 1) / (5 - 2) = 15 / 3 = 5
Next, we can choose any point from the table to find the y-intercept.
Using the point (x=1, y=–4), we can substitute these values into the equation y = mx + b and solve for b:
–4 = 5(1) + b
–4 = 5 + b
b = –4 - 5
b = –9
Therefore, the linear function that models the data is:
y = 5x - 9