Question

Convert r= 2 / 7sinθ−cosθ to rectangular form.

Enter your answer in slope-intercept form by filling in the boxes. Enter values so that fractions are simplified.

Answer 1

The rectangular form of the given equation r= 2 / 7sinθ−cosθ which is in polar form is  7x - y = 2 and the slope-intercept form is y = 7x - 2

How to convert from polar form to rectangular form?

To convert from polar form to rectangular form we simply take the following steps:

1. x = rsinθ
2. y = rcosθ

What is slope-intercept form?

The slope-intercept form is,

y = mx +c

where m is the slope made and c is the intercept both made by the straight line.

In the given question let's first rearrange it,

r × (7sinθ − cosθ) = 2

Multiplying the term (7sinθ−cosθ) with r we get,

7rsinθ - rcosθ = 2

Now we will follow the steps discussed above which is we will put x and y respectively in place of rsinθ and rcosθ.

7x - y = 2

So, the slope-intercept form will be,

y = 7x - 2

Therefore, the rectangular form is 7x - y = 2 and the slope-intercept form is y = 7x - 2.

To know more about the polar form and how to convert it to rectangular form click here - brainly.com/question/27412064

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Answer 2

Let's simplify

Remember that rsinØ is x an rcosØ=y

• r=2/7sinØ-cosØ
• r(7sinØ-cosØ)=2
• 7rsinØ-rcosØ=2
• 7x-y=2

Rectangle form or slope intercept form

• y=7x-2