Respuesta :
Answer:
[tex]y(x)=-\frac{3}{5}x-\frac{1}{5}[/tex]Explanation: We need to find the equation of the line in y-intercept form:
Given the two points:
[tex]\begin{gathered} P_1(3,-2) \\ P_2(-2,1) \end{gathered}[/tex]The standard form of the equation of the line is:
[tex]y(x)=mx+b[/tex]Where:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}\rightarrow slope \\ b\rightarrow y-intercept \end{gathered}[/tex]Now, the last step is to find these unknowns from the given information:
Slope:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{1-(-2)}{-2-(3)}=\frac{1+2}{-2-3}=\frac{3}{-5}=-\frac{3}{5}[/tex]Y-intercept:
We will simply now put one of the points in our standard equation, and extract the y-intercept:
[tex]\begin{gathered} y(x)=mx+b \\ y(3)=-\frac{3}{5}(3)+b=-2 \\ \therefore\rightarrow \\ b=-2+\frac{9}{5}=\frac{-2\cdot5}{5}+\frac{9}{5}=\frac{-10+9}{5}=\frac{-1}{5} \\ y(x)=-\frac{3}{5}x-\frac{1}{5} \end{gathered}[/tex]