How do you find the general form of the line perpendicular to 3x+5y-8=0 that passes through the point (-8,1)?

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Jim G. Share
May 21, 2018

Answer:

#5x-3y+43=0#

Explanation:

#"the general form of the equation of a line is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By+C=0)color(white)(2/2)|)))#

#"where A, B and C are integers with A and B non-zero"#

#"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 "3x+5y-8=0" into this form"#

#"subtract "3x-8" from both sides"#

#rArr5y=-3x+8#

#"divide all terms by 5"#

#rArry=-3/5x+8/5larrcolor(blue)"in slope-intercept form"#

#"with slope m "=-3/5#

#"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/(-3/5)=5/3#

#"now find the equation of the perpendicular line"#

#rArry=5/3x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-8,1)" into the partial equation"#

#1=-40/3+brArrb=3/3+40/3=43/3#

#rArry=5/3x+43/3larrcolor(red)"in slope-intercept form"#

#"rearrange into general form by multiplying all terms by 3"#

#rArr3y=5x+43#

#"subtract "3y" from both sides"#

#rArr5x-3y+43=0larrcolor(red)"in general form"#

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Write your answer here...
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1
May 21, 2018

Answer:

Therefore equation of the perpendicular line is:

#y=5/3x - 37/3#enter image source here

Explanation:

Slope of perpendicular line is negative reciprocal of the original slope of the line.

So given linear equation is:
#3x+5y-8=0# -----> re-write this equation as #y=mx+b# where #m# is the slope of the line and #b# is the y-intercept.

#5y=8-3x#

#5y=-3x+8#

#y=-3/5y + 8/5# -----> Slope of the line is #-3/5# ----> #color(red)(RED -GRAPH)#

So the slope of the perpendicular line is #-1/(-3/5)# = #5/3#

So the equation of the perpendicular line is:
# y = 5/3x + b#

Lets us find #b# from the given points #(-8,1).

# y = 5/3x + b#

#1 = (5/3xx8) + b#

#1 = 40/3+b#

#b =1-40/3#

#b= -37/3#

Therefore equation of the perpendicular line is:

#y=5/3x - 37/3# ----> #color(blue) (BLUE -GRAPH)#

We can draw the graph and check as well (see the attached graphs)

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