Given:
Two points
[tex](1,1)\text{ and (2,-1)}[/tex]To find: The equation of the linear function
Explanation:
Using the two-point formula,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]Here,
[tex]\begin{gathered} x_1=1 \\ y_1=1 \\ x_2=2 \\ y_2=-1 \end{gathered}[/tex]Substituting we get,
[tex]\begin{gathered} \frac{y-1}{-1-1}=\frac{x-1}{2-1} \\ \frac{y-1}{-2}=\frac{x-1}{1} \\ y-1=-2(x-1) \\ y=-2x+2+1 \\ y=-2x+3 \end{gathered}[/tex]Final answer: The equation of the linear function is,
[tex]y=-2x+3[/tex]