1. The problem is to draw the graph of the function $f(x) = -4x$. 2. This is a linear function of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. For $f(x) = -4x$, the slope $m = -4$ and the y-intercept $b = 0$. 4. The slope $-4$ means the line goes down 4 units for every 1 unit it moves to the right. 5. To plot the graph, find intercepts: - The y-intercept is at $(0,0)$. - The x-intercept is also at $(0,0)$ since $f(0) = 0$. 6. Plot another point using the slope: from $(0,0)$ move right 1 unit to $x=1$, then down 4 units to $y=-4$, so point $(1,-4)$. 7. Draw a straight line through points $(0,0)$ and $(1,-4)$. Final answer: The graph is a straight line passing through the origin with slope $-4$.