The graph of r = − 5 2 cos ⁡ ( θ ) + sin ⁡ ( θ ) is a line. Find the y-intercept of this line.

If you have the slope-intercept form y = m x + b, you can substitute y = r sin ⁡ θ and x = r cos ⁡ θ to get r sin ⁡ θ = m ( r cos ⁡ θ ) + b, and then solving for r in terms of θ gives r = b sin ⁡ θ − m cos ⁡ θ .More generally, if the line has equation a x + b y = c, you can solve for r in terms of θ to get r = c a cos ⁡ θ + b sin ⁡ θ .

Solved: "The graph of r = − 5 2..."

Emmy Dillon

Answered question

2022-06-13

The graph of

r = \frac{- 5}{2 \cos (θ) + \sin (θ)}

is a line. Find the y-intercept of this line.

Answer & Explanation

benedictazk

Beginner2022-06-14Added 22 answers

If you have the slope-intercept form

y = m x + b

, you can substitute

y = r \sin θ

and

x = r \cos θ

to get

r \sin θ = m (r \cos θ) + b

, and then solving for

r

in terms of

θ

gives

r = \frac{b}{\sin θ - m \cos θ}

.
More generally, if the line has equation

a x + b y = c

, you can solve for

r

in terms of

θ

to get

r = \frac{c}{a \cos θ + b \sin θ}

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