x y
2
–
14
3
–
16
4
–
18
5
–
20
6
–
22
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Since the y-values increase by a constant amount (8) each time the x-value increases by 1, this is a linear relationship.
Using the slope-intercept form of a linear equation (y = mx + b), where m is the slope and b is the y-intercept, we can find the equation.
To find the slope, we can calculate the change in y divided by the change in x.
Change in y = 16 - 2 = 14
Change in x = 3 - 1 = 2
Slope (m) = (Change in y) / (Change in x) = 14/2 = 7
Now, we can use any point from the data to find the y-intercept (b). Let's use the point (2, 2).
y = mx + b
2 = 7(2) + b
2 = 14 + b
b = -12
Therefore, the linear function that models the data is:
y = 7x - 12