50 POINTS! IM SO CONFUSED I'LL MARK BRAINLIEST!!!! Write a linear function f with f(−4)=2 and f(6)=−3.

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]