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?
The slope of the graph is given by the formula:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
where \((x_1, y_1) = (-4, 4)\) and \((x_2, y_2) = (4, 6)\). Substituting these values, we find
\[m = \frac{{6 - 4}}{{4 - (-4)}} = \frac{2}{8} = \frac{1}{4}.\]Therefore, the slope of the graph is $\boxed{\frac{1}{4}}$.
The y-intercept of the graph is the value of $g(x)$ when $x = 0$. Substituting $x = 0$ into the point-slope form $y - y_1 = m(x - x_1)$, we find
\[y - 4 = \frac{1}{4}(x - (-4)) = \frac{1}{4}(x + 4),\]so $y = \frac{1}{4} x + 5$. Hence, the y-intercept is $\boxed{5}$.