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If g(X) = mx+C , g(-7) = -5 and g(4) = 6, find the values of m and C.​

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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

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