Answer
$r = \frac{6}{3~cos~\theta-2~sin~\theta}$
We can see the graph below:
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0b0ec8f1-ed48-47d5-95f4-18120f21a637/result_image/1529816726.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000506Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=5427d5c91d4671ed25ba338aecdc2448e6d218a0459158d33150f51f93a7b84e)
Work Step by Step
$3x-2y = 6$
$3~r~cos~\theta-2~r~sin~\theta = 6$
$r = \frac{6}{3~cos~\theta-2~sin~\theta}$
We can see the graph below:
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0b0ec8f1-ed48-47d5-95f4-18120f21a637/steps_image/small_1529816726.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000506Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=a0577fb1130c48a986379a92ae94cd8d739ddbbed79ab9f57380fa7de5acea9d)
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