x y
–
7
–
48
–
6
–
42
–
5
–
36
–
4
–
30
–
3
–
24
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
Based on the data given, it appears that the values of y decrease as x increases. Therefore, a linear function (y=mx+b) would be appropriate to model the data.
To find the slope (m) and y-intercept (b) of the linear function, we can use any two points from the given data. Let's use the points (x=-7, y=-48) and (x=-3, y=-24).
Slope (m) = (change in y) / (change in x) = (-24 - (-48)) / (-3 - (-7)) = 24 / 4 = 6.
Using the point (x=-7, y=-48) in the linear equation y=mx+b, we can substitute the values to find the y-intercept (b).
-48 = 6*(-7) + b
-48 = -42 + b
b = -6.
Therefore, the linear function that models the data is y = 6x - 6.