trazar el gráfico de la función $f(x)=-3x-1$.

Explanation:

Step1: Identify slope and y-intercept

The function $f(x)=-3x-1$ follows the slope-intercept form $y=mx+b$, where $m=-3$ (slope) and $b=-1$ (y-intercept, the point $(0, -1)$).

Step2: Plot the y-intercept

Mark the point $(0, -1)$ on the coordinate grid.

Step3: Use slope to find a second point

Slope $m=\frac{\Delta y}{\Delta x}=\frac{-3}{1}$. From $(0, -1)$, move 1 unit right and 3 units down to get the point $(1, -1-3)=(1, -4)$. Alternatively, move 1 unit left and 3 units up to get $(-1, -1+3)=(-1, 2)$.

Step4: Draw the line

Connect the plotted points with a straight line, extending it across the entire grid.

Answer:

The graph is a straight line passing through points such as $(-1, 2)$, $(0, -1)$, and $(1, -4)$, extending infinitely in both directions.