How do you write the polar form of the equation of the line that passes through the points (4,-1) and (-2,3)?

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Answer 1 · 2017-05-30T17:09:40

Please see the explanation.

The slope, m, of the line is:

#m = (3- (-1))/(-2-4)#

#m = 4/-6#

#m = -2/3#

Use the point-slope form of the equation of a line:

#y = m(x-x_1)+y_1#

#y = -2/3(x-4)-1#

Here is a graph of that line:

Desmos.com

Multiply both sides by 3:

#3y = -2(x-4)-1#

Distribute the -2:

#3y = -2x+8-1#

Add 2x to both sides:

#2x+3y = 7#

Substitute #rcos(theta)# for x and #rsin(theta)# for y:

#2rcos(theta)+3rsin(theta) = 7#

Factor out r:

#r(2cos(theta)+3sin(theta)) = 7#

Divide both sides by #(2cos(theta)+3sin(theta))#

#r = 7/(2cos(theta)+3sin(theta))#

Here is a graph of that equation:

Desmos.com