#"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"#
#"to begin obtain the equation in "color(blue)"point-slope form"#
#•color(white)(x)y-b=m(x-a)#
#"where m is the slope and "(a,b)" a point on the line"#
#"to calculate m use the "color(blue)"gradient formula"#
#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#
#"let "(x_1,y_1)=(1,5)" and "(x_2,y_2)=(3,0)#
#m=(0-5)/(3-1)=(-5)/2=-5/2#
#• " Parallel lines have equal slopes"#
#"using "m=-5/2" and "(a,b)=(-1,3)#
#y-3=-5/2(x+1)larrcolor(red)"in point-slope form"#
#"distribute and rearrange for standard form"#
#y-3=-5/2x-5/2#
#y=-5/2x+1/2#
#"multiply all terms by 2"#
#2y=-5x+1#
#5x+2y=1larrcolor(red)"in standard form"#
