2. Let $H \subset \mathbb{R}^2$ be the line $H = \{(a, 2a) : a \in \mathbb{R}\}$. Consider the collection of all translates of $H$; that is all lines with slope 2. Find the equivalence relation on $\mathbb{R}^2$ defined by this partition of $\mathbb{R}^2$.
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The equation of a line with slope m passing through the point (x1, y1) is given by y - y1 = m(x - x1). In this case, since the line passes through the origin (0, 0), the equation of H is y = 2x. Show more…
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