#"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)"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,-5)" and "(x_2,y_2)=(7,-2)#

#rArrm=(-2-(-5))/(7-5)=3/2#

#rArry=3/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute either of the 2 given points into"#

#"the partial equation"#

#"using "(7,-2)" then"#

#-2=21/2+brArrb=-4/2-21/2=-25/2#

#rArry=3/2x-25/2larrcolor(red)"in slope-intercept form"#

#"multiply all terms by 2"#

#rArr2y=3x-25#

#rArr3x-2y=25larrcolor(red)"in standard form"#