Look at this table:
x y
–
5
–
38
–
4
–
31
–
3
–
24
–
2
–
17
–
1
–
10
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Based on the given data, it appears to be a linear relationship between x and y. To find the linear function (y=mx+b), we can use the formula y = mx + b, where m is the slope and b is the y-intercept.
Let's calculate the slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (-5, 38) and (-1, 10):
m = (10 - 38) / (-1 - (-5))
m = (-28) / (4)
m = -7
Now, let's calculate the y-intercept (b) using one of the points (-5, 38):
y = mx + b
38 = -7(-5) + b
38 = 35 + b
38 - 35 = b
3 = b
Therefore, the linear function (y=mx+b) that models the data is:
y = -7x + 3