Given:
[tex]r\text{ = }\frac{7}{6cos\theta\text{ -9sin}\theta}[/tex]
Step 1: Cross-Multiply
[tex]6rcos\theta\text{ - 9rsin}\theta\text{ = 7}[/tex]
By definition:
[tex]\begin{gathered} x\text{ = rcos}\theta \\ y\text{ = rsin}\theta \end{gathered}[/tex]
Step 2: Substitute the expression for x and y:
[tex]6x\text{ - 9y = 7}[/tex]
Hence, the rectangular form of the given polar form:
6x - 9y = 7
