Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r \( \sin \theta=7 \) What is the standard form of the equation in rectangular form?

To transform the polar equation \( r \sin \theta = 7 \) into rectangular coordinates, we use the relationships \( r = \sqrt{x^2 + y^2} \) and \( \sin \theta = \frac{y}{r} \). Substituting these into the equation gives us: \[ r \cdot \frac{y}{r} = 7 \implies y = 7 \] This equation represents a horizontal line at \( y = 7 \) in rectangular coordinates. Now, let's graph it! Imagine a straight line that runs left and right across the coordinate plane like a tightrope. It cuts through the \( y \)-axis at 7, while stretching out infinitely in the \( x \) direction. So, if you were to walk on that line, you'd never stray above or below it—just a perfect, steady stroll!