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So, if we assume the change in ##x## to be ##dx## the corresponding change in ##y## would be ##dy##.So, $$y+dy = 5(x+dx)+3$$ From here we get

$$\frac{dy}{dx}=5$$ From mathematical point of view everything is clear, but can you make me understand this $$\frac{dy}{dx}=5$$ in a more intuitive

way(graphical maybe) or something else.