#"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, obtain the equation in "color(blue)"slope-intercept form"#
#•color(white)(x)y=mx+b#
#"where m is the slope and b the y-intercept"#
#"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)=(5,22)" and "(x_2,y_2)=(3,12)#
#rArrm=(12-22)/(3-5)=(-10)/(-2)=5#
#rArry=5x+blarrcolor(blue)"is the partial equation"#
#"to find b substitute either of the 2 given points into"#
#"the partial equation"#
#"using "(3,12)" then"#
#12=15+brArrb=12-15=-3#
#rArry=5x-3larrcolor(red)"in slope-intercept form"#
#"subtract y and add 3 to both sides"#
#rArr5x-y=3larrcolor(red)"in standard form"#
