The ordered pairs shown in the table are generated by the function g(x).
x g(x)
1 -5
3 -13
5 -21
The function g(x) can be represented by the equation g(x) = ax+ b. Enter the value for a and the value for b in the equation g(x) = ax +b.
a =
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b =
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To find the values for a and b in the equation g(x) = ax + b, we can use the given ordered pairs (1, -5), (3, -13), and (5, -21).
Using the first pair (1, -5), we can substitute x = 1 and g(x) = -5 into the equation to get:
-5 = a(1) + b
-5 = a + b
Using the second pair (3, -13), we can substitute x = 3 and g(x) = -13 into the equation to get:
-13 = a(3) + b
-13 = 3a + b
Using the third pair (5, -21), we can substitute x = 5 and g(x) = -21 into the equation to get:
-21 = a(5) + b
-21 = 5a + b
Now we have a system of equations:
-5 = a + b
-13 = 3a + b
-21 = 5a + b
We can solve this system of equations to find the values of a and b. Subtracting the first equation from the second equation, we get:
-13 - (-5) = 3a - a + (b - b)
-8 = 2a
a = -4
Substituting a = -4 into the first equation -5 = a + b, we get:
-5 = -4 + b
b = -1
Therefore, the values for a and b in the equation g(x) = ax + b are:
a = -4
b = -1