Question

Consider the function k(x) = ax + b, where a and b are constants. If k(2) = 3 and k(3) = 5, what is the value of b?

Answer 1

To find the value of b in the function k(x) = ax + b, we can use the given information. Using the system of equations, we find that a = 2 and b = -1.

Step-by-step explanation:

To find the value of b in the function k(x) = ax + b, we can use the given information.

Since k(2) = 3, we substitute 2 for x in the function:
3 = a(2) + b
3 = 2a + b
Similarly, since k(3) = 5, we substitute 3 for x in the function:
5 = a(3) + b
5 = 3a + b
Now we have a system of two linear equations with two variables.

Subtracting the second equation from the first, we eliminate b:
3 - 5 = 2a - 3a
-2 = -a
Simplifying, we get a = 2.

Now we can substitute this value of a into either of the original equations to solve for b.

Using the first equation:
3 = 2(2) + b
3 = 4 + b
b = -1
Therefore, the value of b is -1.