1. The problem is to understand and graph the linear function $f(x) = -7x + 2$. 2. The formula for a linear function is $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -7$ means the line goes down steeply from left to right. 4. The y-intercept $b = 2$ means the line crosses the y-axis at the point $(0, 2)$. 5. To graph, start at $(0, 2)$ on the y-axis. 6. From there, use the slope $-7$ which means for every 1 unit increase in $x$, $f(x)$ decreases by 7 units. 7. For example, when $x = 1$, $f(1) = -7(1) + 2 = -7 + 2 = -5$. 8. Plot the points $(0, 2)$ and $(1, -5)$ and draw a straight line through them. 9. This line represents the function $f(x) = -7x + 2$ with a steep negative slope and y-intercept at 2.