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If g(x) is a linear function such that g(-3) = 2 and g(1) = -4, find g(7)

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Answer:

-13.

Explanation:

If g(x) is linear function, then'\


g(x)=ax+b.

Since g(-3) = 2 and g(1) = -4, then


  • g(-3)=a\cdot (-3)+b=2;

  • g(1)=a\cdot 1+b=-4.

Subtract from the first equation the second one:


-3a-a=2-(-4),\\ \\-4a=6,\\ \\a=-(3)/(2).

Then
b=-4-a=-4-\left(-(3)/(2)\right)=-(5)/(2).

Hence, the equation of the linear function is


g(x)=-(3)/(2)x-(5)/(2).

Then


g(7)=-(3)/(2)\cdot 7-(5)/(2)=-13.

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