Asked by ik ur cheating
look at this table:
x
-10
-9
-8
-7
-6
y
73
65
57
49
41
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
x
-10
-9
-8
-7
-6
y
73
65
57
49
41
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
Answers
There are no human answers yet.
Answered by
GPT 3.5
To determine whether the function is linear or exponential, we need to find the difference in y-values between each pair of data points. If the differences are consistent, then the function is linear; if the ratios are consistent, then the function is exponential.
Let's find the differences in y-values:
-10: 73
-9: 65
-8: 57
-7: 49
-6: 41
Differences:
73 - 65 = 8
65 - 57 = 8
57 - 49 = 8
49 - 41 = 8
The differences in y-values are consistent, indicating that the function is linear. Now we need to find the slope (m) and the y-intercept (b) for the linear function y=mx+b.
First, calculate the slope:
m = (65-41) / (-9-(-6)) = 8 / -3 = -8/3
Next, substitute one of the points into the equation to find the y-intercept:
73 = (-8/3)(-10) + b
73 = 80/3 + b
73 - 80/3 = b
(219 - 80) / 3 = b
139 / 3 = b
b = 46.33
Therefore, the linear function that models the data is:
y = (-8/3)x + 46.33
Let's find the differences in y-values:
-10: 73
-9: 65
-8: 57
-7: 49
-6: 41
Differences:
73 - 65 = 8
65 - 57 = 8
57 - 49 = 8
49 - 41 = 8
The differences in y-values are consistent, indicating that the function is linear. Now we need to find the slope (m) and the y-intercept (b) for the linear function y=mx+b.
First, calculate the slope:
m = (65-41) / (-9-(-6)) = 8 / -3 = -8/3
Next, substitute one of the points into the equation to find the y-intercept:
73 = (-8/3)(-10) + b
73 = 80/3 + b
73 - 80/3 = b
(219 - 80) / 3 = b
139 / 3 = b
b = 46.33
Therefore, the linear function that models the data is:
y = (-8/3)x + 46.33
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