"the equation of a line in "color(blue)"standard form"the equation of a line in 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"
"the equation of a line in "color(blue)"slope-intercept form" is.
•color(white)(x)y=mx+b
"where m is the slope and b the y-intercept"
"rearrange "4x-8y=1" into this form"
-8y=-4x+1rArry=1/2x-1/8tom=1/2
"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_(color(red)"perpendicular")=-1/(1/2)=-2
rArry=-2x+blarrcolor(blue)"is the partial equation"
"to find b substitute "(1/2,-2/3)" into the partial"
"equation"
-2/3=-1+brArrb=-2/3+1=1/3
rArry=-2x+1/3larrcolor(red)"in slope-intercept form"
"multiply through by 3 to eliminate fraction"
rArr3y=-6x+1
rArr6x+3y=1larrcolor(red)"in standard form"
