How do you find the general form of the line that passes through A(3, -4); perpendicular to the line 2x - 6y = 11?

Question

Abigail Allen · Accepted Answer

#3x+y-5=0# #"the equation of a line in "color(blue)"general form"# is. #color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By+C=0)color(white)(2/2)|)))# #"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 "2x-6y=11" into this form"# #rArr6y=2x-11# #rArry=1/3x-11/6larrcolor(red)"in slope-intercept form"# #rArr"slope "=m=1/3# #"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/(1/3)=-3# #rArry=-3x+b color(blue)" is the partial equation"# #"to find b substitute "(3,-4)" into the partial equation"# #-4=-9+brArrb=5# #rArry=-3x+5larrcolor(red)"in slope-intercept form"# #rArr3x+y-5=0larrcolor(red)"in general form"#

Ethan Adkins · Answer

undefined To find the general form of the line passing through point A(3, -4) and perpendicular to the line 2x - 6y = 11, follow these steps:

1. Determine the slope of the given line by rearranging the equation into slope-intercept form (y = mx + b).
2. The slope of the line perpendicular to the given line will be the negative reciprocal of the slope of the given line.
3. Use the point-slope form of a line (y - y1 = m(x - x1)) with the slope found in step 2 and the coordinates of point A to find the equation of the perpendicular line.
4. Rearrange the equation into general form (Ax + By + C = 0).

Apply these steps to find the general form of the perpendicular line passing through point A(3, -4).