Look at this table:
x y
2
–
17
3
–
22
4
–
27
5
–
32
6
–
37
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the table is best modeled by a linear function or an exponential function, we need to look at the differences in the y-values.
In this case, the differences between the y-values are constant. The differences are 5, which means the table is best represented by a linear function.
To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope (m):
m = (change in y-values) / (change in x-values)
= (y2 - y1) / (x2 - x1)
Using the first two points (2,-17) and (3,-22):
m = (-22 - (-17)) / (3 - 2)
= (-22 + 17) / (3 - 2)
= -5
Now, let's find the y-intercept (b).
We can use the point (2, -17) and plug it into the equation y = mx + b:
-17 = -5(2) + b
-17 = -10 + b
b = -17 + 10
b = -7
Therefore, the linear function that models the data is:
y = -5x - 7