Answer:
-13.
Step-by-step explanation:
If g(x) is linear function, then'\
[tex]g(x)=ax+b.[/tex]
Since g(-3) = 2 and g(1) = -4, then
- [tex]g(-3)=a\cdot (-3)+b=2;[/tex]
- [tex]g(1)=a\cdot 1+b=-4.[/tex]
Subtract from the first equation the second one:
[tex]-3a-a=2-(-4),\\ \\-4a=6,\\ \\a=-\dfrac{3}{2}.[/tex]
Then [tex]b=-4-a=-4-\left(-\dfrac{3}{2}\right)=-\dfrac{5}{2}.[/tex]
Hence, the equation of the linear function is
[tex]g(x)=-\dfrac{3}{2}x-\dfrac{5}{2}.[/tex]
Then
[tex]g(7)=-\dfrac{3}{2}\cdot 7-\dfrac{5}{2}=-13.[/tex]
