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 of a and b in the equation g(x) = ax + b, we can use the given ordered pairs (1, -5), (3, -13), and (5, -21) to create a system of equations.
Using the point (1, -5):
-5 = a(1) + b
-5 = a + b
Using the point (3, -13):
-13 = a(3) + b
-13 = 3a + b
Subtracting the first equation from the second equation:
-13 - (-5) = 3a + b - (a + b)
-8 = 2a
a = -4
Substitute a = -4 back into the first equation:
-5 = -4 + b
b = -1
Therefore, the values of a and b in the equation g(x) = ax + b are:
a = -4
b = -1