The function of x is [tex]\bold{\frac{-1x}{2}}[/tex].
SOLUTION:
Given that, we have to write a linear function f with function of (-4) =2 and function of 6=(−3).
Now, let the linear function be [tex]\text{function of x}=a x+b[/tex]
Then, function of -4 = [tex]a(-4)+b \rightarrow 2=-4 a+b \rightarrow b=2+4a \rightarrow (1)[/tex]
And, function of 6 = [tex]a(6)+b \rightarrow-3=6 a+b \rightarrow b=-3-6a \rightarrow (2)[/tex]
On equating (1) and (2) to find the value of a,
[tex]2+4a=-3-6a[/tex]
On grouping the common terms,
[tex]4a+6a=-3-2 \rightarrow 10a=-5 \rightarrow a=\frac{-5}{10}[/tex]
[tex]\Rightarrow a=\frac{-1}{2} \rightarrow (3)[/tex]
On substituting the value of (3) in (1) we get,
[tex]b=2+4a \rightarrow b=2+4\times\frac{-1}{2} \rightarrow b=2+\frac{-4}{2} \rightarrow b=2+(-2)[/tex]
[tex]\Rightarrow b=0[/tex]
So, the function of x = [tex]\frac{-1x}{2}+0[/tex]
