1. The problem is to understand and analyze the linear function $y=2x+7$. 2. This is a linear equation in slope-intercept form $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m=2$ means for every increase of 1 in $x$, $y$ increases by 2. 4. The y-intercept $b=7$ means the graph crosses the y-axis at the point $(0,7)$. 5. To find the x-intercept, set $y=0$ and solve for $x$: $$0=2x+7$$ $$2x=-7$$ $$x=\frac{-7}{2}$$ 6. The x-intercept is at $\left(-\frac{7}{2},0\right)$. 7. This line has no extrema (no maximum or minimum) because it is a straight line. 8. Summary: slope = 2, y-intercept = 7, x-intercept = $-\frac{7}{2}$. This explains the function $y=2x+7$ clearly and completely.