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Question Number 12013 by tawa last updated on 09/Apr/17

$$\mathrm{The}\mathrm{slope}\mathrm{of}\mathrm{a}\mathrm{curve}\mathrm{is},7\mathrm{x}+3\mathrm{and}\mathrm{it}\mathrm{passes}\mathrm{through}\mathrm{the}\mathrm{point}(2,4),$$$$\mathrm{Find}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{point}$$

Answered by ajfour last updated on 09/Apr/17

$$\frac{dy}{dx}=7x+3$$$$\int dy=\int (7x+3)dx$$$$\Rightarrow y=\frac{7x^2}{2}+3x+C$$$$asitpassesthrough(2,4)$$$$4=\frac{7\times 4}{2}+3\times 2+C$$$$\Rightarrow C=4-20=-16$$$$y=\frac{7x^2}{2}+3x-16.$$

Commented by tawa last updated on 09/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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