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Can someone check my work please?

Convert each polar equation to a rectangular equation. Then determine the graph's slope and y-intercept.
( I'm going to type 'x' instead of theta )
r sin(x- pi/4)=2

r(sin(x- pi/4))=2
r(sinx*cos pi/4 - sin pi/4*cosx)=2
r(sqrt2/2*sin x - sqrt2/2*cos x)=2
sqrt2/2*rsin x - sqrt2/2*rcosx=2
(sqrt2/2*y - sqrt2/2*x=2)^2
1/2(y^2) - 1/2(x^2)= 4
1/2(y^2 - x^2)=4
y^2 - x^2= 8
(y^2= 8 + x^2) sqrt
y= sqrt(8) + x

slope= 1
y-int= sqrt 8

miraculously, you made two major errors that cancelled each other out, and you came up with the right answer.

line 4 can be reduced to √2y - √2x = 4
which convert to y = -x + √8
so your answer is right

why are you squaring the equation in line 5???, you had it!!!

When you square an equation you CANNOT just square each term.
Your left side should have contained 3 terms.
Then in line 9 you cannot take the square root of each term!

eg. √(16+9) is not equal to √16 + √9

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