Convert the rectangular equation to polar form.y = −x

Sure, here are the steps to convert the rectangular equation y = -x to polar form:

Step 1: Write down the rectangular equation: y = -x

Step 2: Recall the polar coordinate system relationships: x = rcos(θ) y = rsin(θ)

Step 3: Substitute the polar relationships into the rectangular equation: rsin(θ) = -rcos(θ)

Step 4: Divide both sides by r (assuming r ≠ 0): sin(θ) = -cos(θ)

Step 5: Divide both sides by cos(θ) (assuming cos(θ) ≠ 0): tan(θ) = -1

Step 6: Solve for θ. The solution to tan(θ) = -1 is θ = 3π/4 + kπ, where k is an integer.

So, the polar form of the equation y = -x is θ = 3π/4 + kπ.