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.
To find the values of a and b in the equation g(x) = ax + b, we can use the given ordered pairs (x, g(x)).
From the table, we can see that when x = 1, g(x) = -5.
Plugging these values into the equation, we get: -5 = a(1) + b.
From the table, we can see that when x = 3, g(x) = -13.
Plugging these values into the equation, we get: -13 = a(3) + b.
Now we have a system of two equations:
-5 = a + b
-13 = 3a + b
We can solve this system of equations to find the values of a and b.
Multiplying the first equation by 3, we get:
-15 = 3a + 3b
Subtracting the second equation from this equation, we eliminate b:
-15 - (-13) = 3a + 3b - (3a + b)
-15 + 13 = 3a + 3b - 3a - b
-2 = 2b
Dividing both sides by 2, we find:
b = -1
Substituting this value back into the first equation, we can find the value of a:
-5 = a + (-1)
-5 + 1 = a
-4 = a
Therefore, the values for a and b in the equation g(x) = ax + b are:
a = -4 and b = -1.