Construct a graph from the following data and consider tangents...

Construct a graph from the following data and consider tangents drawn at $x = 2, 4, 6$, and $8$. Identify the correct equation of the curve and the expression for the slope of the tangent \left(\tan\theta = \dfrac{dy}{dx}\right)$.<br><table style="border: 1px solid black; border-collapse: collapse; width: auto;"><tr><td style="border: 1px solid black; padding: 10px;">$x$</td><td style="border: 1px solid black; padding: 10px;">$1$</td><td style="border: 1px solid black; padding: 10px;">$2$</td><td style="border: 1px solid black; padding: 10px;">$3$</td><td style="border: 1px solid black; padding: 10px;">$4$</td><td style="border: 1px solid black; padding: 10px;">$5$</td><td style="border: 1px solid black; padding: 10px;">$6$</td><td style="border: 1px solid black; padding: 10px;">$7$</td><td style="border: 1px solid black; padding: 10px;">$8$</td><td style="border: 1px solid black; padding: 10px;">$9$</td><td style="border: 1px solid black; padding: 10px;">$10$</td></tr><tr><td style="border: 1px solid black; padding: 10px;">$y$</td><td style="border: 1px solid black; padding: 10px;">$2$</td><td style="border: 1px solid black; padding: 10px;">$8$</td><td style="border: 1px solid black; padding: 10px;">$18$</td><td style="border: 1px solid black; padding: 10px;">$32$</td><td style="border: 1px solid black; padding: 10px;">$50$</td><td style="border: 1px solid black; padding: 10px;">$72$</td><td style="border: 1px solid black; padding: 10px;">$98$</td><td style="border: 1px solid black; padding: 10px;">$128$</td><td style="border: 1px solid black; padding: 10px;">$162$</td><td style="border: 1px solid black; padding: 10px;">$200$</td></tr></table>$