Determine the equation of a linear function from two points Precalculus

Determine the equation of the following linear functions.

f goes by A\left(-2,-1\right) and B\left(2{,}4\right).

f\left(x\right)=2x+1

f\left(x\right) = -\dfrac{5}{4}x + \dfrac{3}{2}

f\left(x\right) = \dfrac{5}{4}x - \dfrac{3}{2}

f\left(x\right) = \dfrac{5}{4}x + \dfrac{3}{2}

f passes through \left(-1{,}1\right) and (1,0).

f\left(x\right)=-\dfrac{1}{2}x+\dfrac{1}{2}

f\left(x\right)=\dfrac{1}{2}x+\dfrac{1}{2}

f\left(x\right)=-\dfrac{1}{2}x-\dfrac{1}{2}

f\left(x\right)=\dfrac{1}{2}x-\dfrac{1}{2}

f passes through \left(3{,}2\right) and (3,-4)

x=-4

x=3

f\left(x\right) =x-1

f\left(x\right)=-x+1

f goes by \left(3{,}0\right) and \left(0,-2\right)

f\left(x\right) = -\dfrac{2}{3}+2

f\left(x\right) = \dfrac{2}{3}x-\dfrac{2}{3}

f\left(x\right) = \dfrac{2}{3}x+2

f\left(x\right) = \dfrac{2}{3}x-2

f passes through \left(1,-1\right) and \left(-2,-1\right)

f\left(x\right)=x-1

f(x)=x+1

f(x)=−1

f\left(x\right)=-2

f goes through \left(-1{,}1\right) and \left(1,-1\right)

f\left(x\right)=-x

f\left(x\right)=x

f(x)=x−1

f(x)=x+1

f passes through \left(1{,}2\right) and \left(2{,}3\right)

f\left(x\right) = x-1

f\left(x\right) = x+1

f\left(x\right) = -x+1

f\left(x\right) = -x-1