The equation of a line given two points A and B is calculated by the formula
[tex]\begin{gathered} A(x_1,y_1);B(x_2,y_2) \\ \text{the equation of the line AB is} \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]From the graph given, we have two points.
[tex]A(-5,3);B(5,-2)[/tex]Substituting the values of the given points into the formula to get the equation of line
[tex]x_1=-5;y_1=3;x_2=5;y_2=-2\frac{\square}{\square}[/tex][tex]\begin{gathered} \frac{y-3}{x-(-5)}=\frac{-2-3}{5-(-5)} \\ \frac{y-3}{x+4}=\frac{-5}{5+5} \\ \frac{y-3}{x+4}=-\frac{5}{10} \end{gathered}[/tex][tex]\begin{gathered} \frac{y-3}{x+4}=\frac{-1}{2} \\ 2(y-3)=-1(x+4) \\ 2y-6=-x-4 \\ 2y+x=-4+6 \\ 2y+x=2 \end{gathered}[/tex][tex]\begin{gathered} 2y=2-x \\ y=\frac{2}{2}-\frac{x}{2} \\ y=1-\frac{x}{2} \end{gathered}[/tex]Hence, the equation of the line is y=1-x/2
