Question

WILL MARK BRAINLIEST !!!!!
The function g is defined by the equation g(x) = ax + b, where a and b are constants.
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If g(4) = -4 and g(6) = 3, what is the value of g(-4) ? (Show all your work)

Answer 1

Answer:

g(- 4) = - 32

Step-by-step explanation:

substitute x = 4 , g(4) = - 4 into g(x)

4a + b = - 4 → (1)

substitute x = 6 , g(6) = 3 into g(x)

6a + b = 3 → (2)

subtract (1) from (2) term by term to eliminate b

2a + 0 = 3 - (- 4)

2a = 3 + 4 = 7 ( divide both sides by 2 )

a = 3.5

substitute a = 3.5 into (1) and solve for b

4(3.5) + b = - 4

14 + b = - 4 ( subtract 14 from both sides )

b = - 18

Then

g(x) = 3.5x - 18 , so

g(- 4) = 3.5(- 4) - 18 = - 14 - 18 = - 32

Answer 2

Answer:

g(-4) = -32

Explanation:

g(x) = ax + b

If g(4) = -4

-4 = a(4) + b

4a + b = -4

b = -4 -4a ............equation 1

If g(6) = 3

3 = a(6) + b

6a + b = 3

b = 3 - 6a ............equation 2

solving simultaneously:

3 - 6a =  -4 -4a

-6a + 4a = -4 -3

-2a = -7

a = 3.5

b = 3 - 6a

b = 3 -6(3.5)

b = -18

equation found: g(x) = 3.5x - 18

then g(-4)

3.5(-4) - 18

-32