Question

Really need to someone to break this down so I can understand it

Answer 1

Answer:

Slope is 4/3

Step-by-step explanation:

Slope is the derivative of the equation:

$y = \frac{1}{3} {x}^{2} - 2x + 15 \\ \\ \frac{dy}{dx} = \frac{1}{3} (2x) - 2 + 0 \\ \\ \frac{dy}{dx} = \frac{2}{3} x - 2$

At point (5, 7), x is 5:

$\frac{dy}{dx} = (\frac{2}{3} \times 5) - 2 \\ \\ \frac{dy}{dx} = \frac{10}{3} - 2 \\ \\ \frac{dy}{dx} = \frac{10 - 6}{3} \\ \\ \frac{dy}{dx} = \frac{4}{3}$