#"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"#
#"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"#
#"rearrange "6x-4y=-9" into this form"#
#"subtract "6x" from both sides"#
#rArr-4y=-6x-9#
#"divide all terms by "-4#
#rArry=3/2x+9/4larrcolor(blue)"in slope-intercept form"#
#"with slope m "=3/2#
#"given a line with slope m then the slope of a line"#
#"perpendicular to it is"#
#•color(white)(x)m_(color(red)"perpendicular")=-1/m#
#rArrm_("perpendicular")=-1/(3/2)=-2/3#
#rArry=-2/3x+blarrcolor(blue)"is the partial equation"#
#"to find b substitute "(4,-1)" into the partial equation"#
#-1=-8/3+brArrb=-1+8/3=5/3#
#rArry=-2/3x+5/3larrcolor(blue)"in slope intercept form"#
#"multiply all terms by "3#
#rArr3y=-2x+5#
#"add "2x" to both sides"#
#rArr2x+3y=5larrcolor(red)"in standard form"#
