Look at this table:
x y
–
3 30
–
2 23
–
1 16
0 9
1 2
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Based on the given table, it appears that the relationship between x and y is linear.
To find the linear function that models the data, we can calculate the slope (m) and y-intercept (b) using two pairs of values from the table.
Using the points (x=-3, y=30) and (x=-2, y=23), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (23 - 30) / (-2 - (-3))
m = (23 - 30) / (-2 + 3)
m = -7 / 1
m = -7
Now, we plug in the slope (m) and one of the points into the slope-intercept form (y = mx + b) to find the y-intercept (b). Let's use the point (x=-3, y=30):
30 = (-7)(-3) + b
30 = 21 + b
b = 30 - 21
b = 9
Therefore, the linear function that models the data is:
y = -7x + 9