The equation of the line passing through the two points is;
[tex]y\text{ = -2x-1}[/tex]Here, we want to get the equation of the line that passes through the two given points
The general form of the equation is;
[tex]\text{y = mx + b}[/tex]where m is the slope and b is the y-intercept
To get the slope, we use the slope equation
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)\text{ = (-1,1)} \\ (x_2,y_2)\text{ = (3,-7)} \\ m\text{ = }\frac{-7-1}{3-(-1)}\text{ = }\frac{-8}{4}\text{ = -2} \end{gathered}[/tex]To get the y-intercept, we will need to substitute the coordinates of any of the points;
[tex]\begin{gathered} y\text{ = -2x + b} \\ \text{substitute x = -1 and y = 1} \\ 1\text{ = -2(-1) + b} \\ 1\text{ = 2 + b} \\ b\text{ = 1-2 = -1} \\ \\ \end{gathered}[/tex]The equation of the line is thus;
[tex]y\text{ = -2x-1}[/tex]