Determining the function equation

General line equation:

$y=m\cdot x+ty=m\backslash cdot\; x+t$

Substitute $tt$ into the line equation.

$f(x)=m\cdot x-1f(x)=m\backslash cdot\; x-1$

Now plug the point $PP$ into $f(x)f(x)$.

$3=m\cdot 2-13=m\backslash cdot2-1$

Solve for $mm$.

$m=(3+1):2=2m=(3+1):2=2$

$f(x)=2x-1f(x)=2x-1$

Plot:

Determining the function equation

General line equation:

$y=m\cdot x+ty=m\backslash cdot\; x+t$

Substitute $tt$ into the line equation.

$f(x)=m\cdot x+3f(x)=m\backslash cdot\; x+3$

Now plug the point $PP$ into $f(x)f(x)$.

$-3=m\cdot (-4)+3-3=m\backslash cdot(-4)+3$

Solve for $mm$.

$m=\frac{-6}{-4}=\frac{3}{2}m=\backslash frac\{-6\}\{-4\}=\backslash frac\{3\}\{2\}$

$f(x)=\frac{3}{2}x+3f(x)=\backslash frac\{3\}\{2\}x+3$

Plot: