Question

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

Answer 1

-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.`