Question

What is the linear function of f-10)=12 and f(16)=-1

Answer 1

f(-10)=12,      x = -10, y = 12

f(16)=-1,        x = 16, y = -1.

so, we have two points, let's check with that,

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -10 &,& 12~) % (c,d) &&(~ 16 &,& -1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-12}{16-(-10)}\implies \cfrac{-1-12}{16+10} \\\\\\ \cfrac{-13}{26}\implies -\cfrac{1}{2}$

$\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)} y-12=-\cfrac{1}{2}[x-(-10)] \\\\\\ y-12=-\cfrac{1}{2}(x+10)\implies y-12=-\cfrac{1}{2}x-5\implies y=-\cfrac{1}{2}x+7$