Look at this table:
x y
–
9
–
38
–
8
–
33
–
7
–
28
–
6
–
23
–
5
–
18
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the data looks more linear or exponential, let's plot the values of x and y.
x y
-9
-38
-8
-33
-7
-28
-6
-23
-5
-18
Based on the data points, it appears to be a linear relationship.
To find the equation of the line, we need to find the slope (m) and y-intercept (b) using two of the given points. Let's use the points (-9, -38) and (-5, -18).
Using the formula for slope:
m = (y2 - y1) / (x2 - x1)
m = (-18 - (-38)) / (-5 - (-9))
m = (-18 + 38) / (-5 + 9)
m = 20 / 4
m = 5
Now, we can use the slope (m) and one of the points to find the y-intercept (b). Let's use the point (-9, -38).
Using the formula:
y = mx + b
-38 = 5(-9) + b
-38 = -45 + b
b = -38 + 45
b = 7
Therefore, the linear equation that models the data is y = 5x + 7.