#" the equation of a line in "color(blue)"standard form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))#
where A is a positive integer and B, C are integers.
#"firstly express the equation in "color(blue)"point slope form"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1)" a point on the line"#
#"here " m=-1/3" and " (x_1,y_1)=(-3,-5)#
#rArry-(-5)=-1/3(x-(-3))#
#rArry+5=-1/3(x+3)larrcolor(red)" in point-slope form"#
#"rearranging into standard form"#
#y+5=-1/3x-1larr" distributing"#
#"add " 1/3x" to both sides"#
#1/3x+y+5=-1#
#"subtract 5 from both sides"#
#1/3x+y=-6#
#"multiply through by 3"#
#x+3y=-18larrcolor(red)" in standard form"#
