By translating the line y = - 2x along the vector a = (2,1), the linear equation is? | Math enthusiast | Mathematical art

By translating the line y = - 2x along the vector a = (2,1), the linear equation is?

Let (a, b) be a point of the original straight line and (a + 2, B + 1) = (x, y) after translation,
Then a + 2 = x, a = X-2 (1)
b+1=y b=y-1 (2)
Substituting (a, b) into the linear equation y = - 2x, B = - 2A
Substituting (1) (2) into the formula Y-1 = - 2 (X-2)
y=-2x+5
That's what we want

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