Look at this table:
x y
–
8
–
43
–
7
–
38
–
6
–
33
–
5
–
28
–
4
–
23
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the data can be modeled by a linear or an exponential function, let's plot the points on a graph.
x | y
--------------
-8 |
-7 |
-6 |
-5 |
-4 |
From the given data, we can see that the x-values decrease by 1 each time, and the y-values decrease by 5 each time. Therefore, we can determine that the relationship between x and y is linear.
We can find the equation of the line using the formula y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we choose two points from the table. Let's choose the points (-8, 43) and (-7, 38).
slope, m = (change in y)/(change in x)
= (38 - 43)/(-7 - (-8))
= (-5)/1
= -5
Now, we can substitute the slope (-5) and one of the points (-8, 43) into the equation y = mx + b to solve for b.
43 = (-5)(-8) + b
43 = 40 + b
b = 3
Thus, the linear function that models the data is:
y = -5x + 3