Connecting $to$ a Calculus Concept; Concavity

The function $f(x)=x^{2}is$ concave $up.$ One way $to$ define this property for the finction

$f(x)=x^{2}is$: $IfP=(a,a^2)$ and $Q=(b,b^2)$ are two unique points $on$ the graph $off(x)=x^2$

then the line segment $\frac{?}{\text{b}\text{a}\text{r}}(PQ)a$ and $bf(x)=x^2,$

$(a)$ Sketch a graph that illustrates the statement above.

$(b)$ Find the slope $of$ the line that passes through any points $P$ and $Q.$ Notice anything

interesting about the simplified value for the slope? Explain. Verify $it$ with $an$ example.