Question

50 POINTS! IM SO CONFUSED I'LL MARK BRAINLIEST!!!!

Answer 1

The function of x is $\bold{\frac{-1x}{2}}$.

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 $\text{function of x}=a x+b$

Then, function of -4 = $a(-4)+b \rightarrow 2=-4 a+b \rightarrow b=2+4a \rightarrow (1)$

And, function of 6 = $a(6)+b \rightarrow-3=6 a+b \rightarrow b=-3-6a \rightarrow (2)$

On equating (1) and (2) to find the value of a,

$2+4a=-3-6a$

On grouping the common terms,

$4a+6a=-3-2 \rightarrow 10a=-5 \rightarrow a=\frac{-5}{10}$

$\Rightarrow a=\frac{-1}{2} \rightarrow (3)$

On substituting the value of (3) in (1) we get,

$b=2+4a \rightarrow b=2+4\times\frac{-1}{2} \rightarrow b=2+\frac{-4}{2} \rightarrow b=2+(-2)$

$\Rightarrow b=0$

So, the function of x = $\frac{-1x}{2}+0$