Question

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

Answer 1

Please see the explanation.

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:

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: