Answer:
So, the values of m and C are:
m = 1
C = 2
Therefore, the equation g(x) is:
g(x) = x + 2
Explanation:
To find the values of m and C, we can use the given information:
g(-7) = -5:
This means when x = -7, the value of g(x) is -5. We can use this information to form an equation:
-5 = m(-7) + C
g(4) = 6:
This means when x = 4, the value of g(x) is 6. We can use this information to form another equation:
6 = m(4) + C
Now, we have a system of two equations with two variables (m and C):
-5 = -7m + C
6 = 4m + C
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:
Step 1: Multiply both sides of equation 1 by 4 and equation 2 by 7 to eliminate C:
-20 = -28m + 4C
42 = 28m + 7C
Step 2: Add the two equations to eliminate m:
-20 + 42 = -28m + 4C + 28m + 7C
22 = 11C
Step 3: Solve for C:
C = 22/11
C = 2
Now that we have the value of C, we can substitute it back into either equation 1 or 2 to solve for m. Let's use equation 1:
-5 = -7m + 2
Step 4: Solve for m:
-7m = -5 - 2
-7m = -7
m = -7/-7
m = 1
So, the values of m and C are:
m = 1
C = 2
Therefore, the equation g(x) is:
g(x) = x + 2