The graph of linear function `g` passes through the points `\left(-4,\ 4\right)`and `\left(4,\ 6\right),`as shown. What are the slope and y-intercept of the graph `g`?
Using the two points $\left( -4, 4 \right)$ and $\left( 4, 6 \right),$ we can compute the slope of the line as
\[\frac{6 - 4}{4 - (-4)} = \frac{2}{8} = \frac{1}{4}.\]Therefore, the slope is $\boxed{\frac{1}{4}}.$
The line passes through $\left( -4, 4 \right),$ so it satisfies the equation
\[y - 4 = \frac{1}{4} (x + 4).\]Then $y - 4 = \frac{1}{4} x + 1,$ which simplifies to $y = \frac{1}{4} x + 5.$ Therefore, the $y$-intercept is $\boxed{5}.$