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

2 Answers
May 21, 2018

Therefore equation of the perpendicular line is:

y=5/3x - 37/3enter 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)

May 21, 2018

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"