Look at this table:
x y
–
2 1.5
–
1
–
2.6
0
–
6.7
1
–
10.8
2
–
14.9
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 exponential function, we can plot the points and see if there is a consistent pattern or trend.
Upon plotting the points, it appears that the data follows a linear pattern. As the x-values increase, the y-values consistently decrease at a relatively constant rate.
Since the data can be modeled by a linear function, we can find the equation of the line by finding the slope (m) and y-intercept (b). To find the slope, we can select two points from the table and use the formula:
m = (change in y) / (change in x)
Let's use the points (0, -6.7) and (1, -10.8):
m = (-10.8 - (-6.7)) / (1 - 0)
m = -4.1
Next, we can use the slope-intercept form of a linear equation, y = mx + b, and substitute the slope and one point (let's use (2, -14.9)) to solve for the y-intercept:
-14.9 = -4.1(2) + b
-14.9 = -8.2 + b
b = -14.9 + 8.2
b = -6.7
Therefore, the linear function that models the data is:
y = -4.1x - 6.7