#"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"#