graph the line using the slope and y - intercept. graph the line through the point (0, - 1), having a slope…

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We are given the point $(0,-1)$ and slope $m=-3$. The x - coordinate of the given point is 0, so the y - coordinate of the point is the y - intercept. So $b=-1$ and $m = - 3$.

Step2: Write the equation of the line

Substitute $m=-3$ and $b = - 1$ into $y=mx + b$. We get $y=-3x-1$.

Step3: Plot the y - intercept

First, plot the point $(0,-1)$ on the y - axis. This is where the line crosses the y - axis.

Step4: Use the slope to find another point

The slope $m=-3=\frac{\Delta y}{\Delta x}$. From the point $(0,-1)$, move 1 unit to the right (increase $x$ by 1) and 3 units down (decrease $y$ by 3) to get the point $(1,-4)$.

Step5: Draw the line

Draw a straight line passing through the points $(0,-1)$ and $(1,-4)$.

Answer:

The line with equation $y=-3x - 1$ is drawn passing through the points $(0,-1)$ and $(1,-4)$.