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Unformatted text preview: is on the line, it must be the case that y = mx + b . Now, the slope of the tangent line to y = mx + b at the point ( x ,y ) is given by f ( x ). By deﬁnition, f ( x ) = lim h → f ( x + h )-f ( x ) h = lim h → [ m ( x + h ) + b ]-[ mx + b ] h = lim h → ( mx + mh + b )-( mx + b ) h = lim h → mh h = lim h → m = m. Therefore, by the point-slope formula, the tangent line is given by y-y = m ( x-x ) . 1 Using the fact that y = mx + b , this becomes y-mx-b = mx-mx . Adding mx + b to both sides tells us that the tangent line is y = mx + b, as desired. 2...
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