The midpoint

The midpoint of (2, 5) and (8, y) is (5, -1). Find the line equation in slope-intercept form.

Result

y =  -7
f = (Correct answer is: -2x+9)

Solution:

$$\begin{gathered} y=f(x)=k\cdot x+q \\ {m}_x={\displaystyle \frac{2+8}{2}}=5 \\ {m}_y={\displaystyle \frac{5+y}{2}}=-1 \\ 5+y=(-1)\cdot 2 \\ y=-7 \end{gathered}$$

$$\begin{gathered} 5=k\cdot 2+q \\ y=k\cdot 8+q \\ 5=k\cdot 2+q \\ (-7)=k\cdot 8+q \\ 2k+q=5 \\ 8k+q=-7 \\ k=-2 \\ q=9 \\ f(x)=k\cdot x+q \\ f=-2x+9 \end{gathered}$$

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