Question

# Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept. r\sin(0-\frac{\pi}{4})=2

Equations
Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept.
$$r\sin(0-\frac{\pi}{4})=2$$

2021-06-12
Step 1
Given polar equation is:
$$r\sin(0-\frac{\pi}{4})=2$$
Step 2
To convert polar equation to a rectangular equation,
put $$r=\sqrt{x^{2}+y^{2}}\ and\ 0=\frac{y}{x}$$
$$\sqrt{x^{2}+y^{2}} \sin (\tan^{-1}(\frac{y}{x})-\frac{\pi}{4})=2$$
$$\sin(\tan^{-1}(\frac{y}{x})-\frac{\pi}{4})=\frac{2}{\sqrt{x^{2}+y^{2}}}$$
$$\tan^{-1}(\frac{y}{x})-\frac{\pi}{4}=\sin^{-1}(\frac{2}{\sqrt{x^{2}+y^{2}}})$$
$$\tan^{-1}(\frac{y}{x})=\sin^{-1}(\frac{2}{\sqrt{x^{2}+y^{2}}})+\frac{\pi}{4}$$