The equation LaTeX: Ax+By=10A x + B y = 10 goes through the coordinates (6, 5) and (-2, -5).

Answer:A=5 and B=-4.Step-by-step explanation:The equation of line is[tex]Ax+By=10[/tex]             .... (1)If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The line passes through the points (6, 5) and (-2, -5). So, the equation of line is[tex]y-5=\frac{-5-5}{-2-6}(x-6)[/tex][tex]y-5=\frac{-10}{-8}(x-6)[/tex][tex]y-5=\frac{5}{4}(x-6)[/tex]Multiply both sides by 4.[tex]4(y-5)=5(x-6)[/tex][tex]4y-20=5x-30[/tex][tex]-20+30=5x-4y[/tex][tex]10=5x-4y[/tex][tex]5x-4y=10[/tex]              .... (2)On comparing (1) and (2) we get[tex]A=5,B=-4[/tex]Therefore, A=5 and B=-4.