Respuesta :
Answer:
The equation of the line that passes through the two points is;
[tex]y=\frac{3}{8}x+\frac{25}{8}[/tex]Explanation:
Given the two points;
[tex](-3,2)\text{ and }(-11,-1)[/tex]Firstly, let us find the slope of the line;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the given points, we have;
[tex]\begin{gathered} m=\frac{-1-2}{-11-(-3)}=\frac{-3}{-8} \\ m=\frac{3}{8} \end{gathered}[/tex]Then to get the equation let us substitute the slope and the first point into the point-slope form of equation of line;
[tex]y-y_1=m(x-x_1)[/tex]Substituting and simplifying;
[tex]\begin{gathered} y-2=\frac{3}{8}(x-(-3)) \\ y-2=\frac{3}{8}(x+3) \\ y-2=\frac{3}{8}x+\frac{9}{8} \\ y=\frac{3}{8}x+\frac{9}{8}+2 \\ y=\frac{3}{8}x+\frac{25}{8} \end{gathered}[/tex]Therefore, the equation of the line that passes through the two points is;
[tex]y=\frac{3}{8}x+\frac{25}{8}[/tex]