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

Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept.
$r\mathrm{sin}\left(0-\frac{\pi }{4}\right)=2$
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Step 1
Given polar equation is:
$r\mathrm{sin}\left(0-\frac{\pi }{4}\right)=2$
Step 2
To convert polar equation to a rectangular equation,
put
$\sqrt{{x}^{2}+{y}^{2}}\mathrm{sin}\left({\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)-\frac{\pi }{4}\right)=2$
$\mathrm{sin}\left({\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)-\frac{\pi }{4}\right)=\frac{2}{\sqrt{{x}^{2}+{y}^{2}}}$
${\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)-\frac{\pi }{4}={\mathrm{sin}}^{-1}\left(\frac{2}{\sqrt{{x}^{2}+{y}^{2}}}\right)$
${\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)={\mathrm{sin}}^{-1}\left(\frac{2}{\sqrt{{x}^{2}+{y}^{2}}}\right)+\frac{\pi }{4}$
Jeffrey Jordon