The equation of a line through two points (x₁,y₁) and (x₂,y₂) is given by the formula:
[tex]y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)[/tex]
The given points are (-1,3) and (2,2).
Substitute the points (x₁,y₁)=(-1,3) and (x₂,y₂)=(2,2) into the formula:
[tex]y-3=(\frac{2-3}{2-(-1)})(x-(-1))[/tex]
Simplify the equation:
[tex]\begin{gathered} y-3=\frac{-1}{2+1}(x+1) \\ \Rightarrow y-3=\frac{-1}{3}(x+1) \\ \Rightarrow y-3=-\frac{1}{3}x-\frac{1}{3} \\ \Rightarrow y=-\frac{1}{3}x-\frac{1}{3}+3 \\ \Rightarrow y=-\frac{1}{3}x+\frac{8}{3} \end{gathered}[/tex]
The required equation is y=-1/3 x+ 8/3.
