1. **State the problem:** We are given a graph of a function $f(x)$ which is a straight line descending from top left to bottom right. 2. **Identify key points from the graph:** The line crosses the y-axis at $y=5$, so the y-intercept is $(0,5)$. 3. **Note special points:** There is an open circle at $(-5,5)$ and a filled circle at $(-5,1)$, indicating a jump or discontinuity at $x=-5$. 4. **Find the slope of the line segment for $x > -5$:** Using points $(0,5)$ and $(-5,1)$, $$m=\frac{1-5}{-5-0}=\frac{-4}{-5}=\frac{4}{5}$$ 5. **Write the equation of the line for $x > -5$ using point-slope form:** $$y - 5 = \frac{4}{5}(x - 0)$$ $$y = \frac{4}{5}x + 5$$ 6. **Evaluate $f(7)$:** Since $7 > -5$, use the equation above: $$f(7) = \frac{4}{5} \times 7 + 5 = \frac{28}{5} + 5 = \frac{28}{5} + \frac{25}{5} = \frac{53}{5} = 10.6$$ **Final answer:** $$f(7) = 10.6$$