Question
Write a linear function F with the values f(6)=8and f(9)=3
Answers
Answered by
GPT 3.5
To write a linear function, we can use the formula for a straight line:
f(x) = mx + b
To find the values of m and b, we can use the given information: f(6) = 8 and f(9) = 3.
Plugging in f(6) = 8:
8 = 6m + b
Plugging in f(9) = 3:
3 = 9m + b
Now, we have a system of two equations:
6m + b = 8
9m + b = 3
Subtracting the first equation from the second equation, we can eliminate b:
(9m + b) - (6m + b) = 3 - 8
3m = -5
m = -5/3
Plugging in the value of m into the first equation, we can solve for b:
6(-5/3) + b = 8
-10 + b = 8
b = 18
So, the linear function F with the given values is:
f(x) = (-5/3)x + 18
f(x) = mx + b
To find the values of m and b, we can use the given information: f(6) = 8 and f(9) = 3.
Plugging in f(6) = 8:
8 = 6m + b
Plugging in f(9) = 3:
3 = 9m + b
Now, we have a system of two equations:
6m + b = 8
9m + b = 3
Subtracting the first equation from the second equation, we can eliminate b:
(9m + b) - (6m + b) = 3 - 8
3m = -5
m = -5/3
Plugging in the value of m into the first equation, we can solve for b:
6(-5/3) + b = 8
-10 + b = 8
b = 18
So, the linear function F with the given values is:
f(x) = (-5/3)x + 18