1. The problem is to analyze the linear function given by the equation $y = 15x + 40$. 2. This is a linear function of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = 15$ means the line rises 15 units vertically for every 1 unit it moves horizontally. 4. The y-intercept $b = 40$ means the line crosses the y-axis at the point $(0, 40)$. 5. To find the x-intercept, set $y = 0$ and solve for $x$: $$0 = 15x + 40$$ $$15x = -40$$ $$x = \frac{-40}{15}$$ $$x = \cancel{\frac{-40}{\cancel{15}}} \Rightarrow x = -\frac{8}{3}$$ 6. So the x-intercept is at $\left(-\frac{8}{3}, 0\right)$. 7. Since this is a linear function, it has no extrema (no maximum or minimum points). 8. Summary: - Slope: 15 - Y-intercept: $(0, 40)$ - X-intercept: $\left(-\frac{8}{3}, 0\right)$ This completes the analysis of the linear function $y = 15x + 40$.