what is the linear function of f(1/2)=-6 and f(4)=-3

f(1/2)=-6,   x = 1/2,   y = -6

f(4)=-3,      x = 4,      y = -3

and here, we'll do the same as well

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ \frac{1}{2} &,& -6~) % (c,d) &&(~ 4 &,& -3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-(-6)}{4-\frac{1}{2}}\implies \cfrac{-3+6}{4-\frac{1}{2}} \\\\\\ \cfrac{\quad 3\quad }{\frac{7}{2}}\implies \cfrac{3}{1}\cdot \cfrac{2}{7}\implies \cfrac{6}{7}[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-6)=\cfrac{6}{7}\left(x-\cfrac{1}{2} \right) \\\\\\ y+6=\cfrac{6}{7}x-\cfrac{3}{7}\implies y=\cfrac{6}{7}x-\cfrac{3}{7}-6\implies y=\cfrac{6}{7}x-\cfrac{45}{7}[/tex]