x y
–
- 2
–
-13
–
-1
–
-9
0
–
-5
1
–
-1
2 3
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
To determine whether the data can be modeled by a linear or exponential function, we can plot the points on a graph and analyze the shape of the curve.
Plotting the points:
(0, -2)
(-1, -13)
(-1, -9)
(0, -5)
(1, -1)
(2, 3)
Based on the plotted points, it appears that the data follows a linear pattern, as the points seem to form a straight line. Therefore, we can model the data with a linear function of the form y = mx + b.
To find the equation of the linear function, we need to determine the values of m and b. Using two points from the data, we can calculate the slope (m) and substitute it into the equation.
Let's use the points (0, -2) and (2, 3).
Slope (m) = (change in y) / (change in x)
m = (3 - (-2)) / (2 - 0) = 5/2
Now that we have the slope, we can use any point from the data to find the y-intercept (b). Let's use the point (0, -2).
y = mx + b
-2 = (5/2)(0) + b
-2 = b
Therefore, the linear function that models the data is y = (5/2)x - 2.