–
6 22
–
5 20
–
4 18
–
3 16
–
2 14
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
In this case, we can see that both the x-values and y-values are decreasing as we move down the table. This suggests that the data may be modeled by a linear function.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose two points from the table to calculate the slope. We can use the first two points: (6, 22) and (5, 20).
m = (20 - 22) / (5 - 6)
= -2 / -1
= 2
Now that we have the slope, we can use one of the points to solve for the y-intercept (b). Let's use the first point: (6, 22).
22 = 2(6) + b
22 = 12 + b
b = 22 - 12
b = 10
Therefore, the linear function that models the data is:
y = 2x + 10