#"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"#

#"first, obtain the equation in "color(blue)"slope-intercept form"#

#•color(white)(x)y=mx+c#

#"where m is the slope and c 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,-2)" and "(x_2,y_2)=(-5,4)#

#m=(4-(-2))/(-5-5)=6/(-10)=-3/5#

#y=-3/5x+clarrcolor(blue)"is the partial equation"#

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

#"the partial equation"#

#"using "(5,-2)" then"#

#-2=-3+crArrc=-2+3=1#

#y=-3/5x+1larrcolor(red)"in slope-intercept form"#

#"multiply all terms by 5"#

#5y=-3x+5#

#"add "3x" to both sides"#

#3x+5y=5larrcolor(red)"in standard form"#