Question

graph the line. \\( y = -3x - 1 \\)

Explanation:

Step1: Identify the slope and y-intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-3x - 1\), the slope \(m=-3\) and the y - intercept \(b=-1\). This means the line crosses the y - axis at the point \((0,-1)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,-1)\) (since when \(x = 0\), \(y=-1\)) and mark it.

Step3: Use the slope to find another point

The slope \(m=-3=\frac{-3}{1}\). The slope is the ratio of the change in \(y\) to the change in \(x\) (\(\frac{\Delta y}{\Delta x}\)). Starting from the y - intercept \((0,-1)\), to find the next point, we move down 3 units (because \(\Delta y=- 3\)) and then 1 unit to the right (because \(\Delta x = 1\)). So from \((0,-1)\), moving down 3 units gives \(y=-1-3=-4\) and moving right 1 unit gives \(x = 0 + 1=1\). So the new point is \((1,-4)\). We can also move up 3 units and left 1 unit from the y - intercept. Moving up 3 units from \((0,-1)\) gives \(y=-1 + 3=2\) and moving left 1 unit gives \(x=0-1=-1\), so the point \((-1,2)\) is also on the line.

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \((0,-1)\), \((1,-4)\), \((-1,2)\)) to graph the line \(y=-3x - 1\).

Answer:

To graph \(y = - 3x-1\):

1. Plot the y - intercept \((0,-1)\).
2. Use the slope \(-3\) to find additional points (e.g., \((1,-4)\) or \((-1,2)\)).
3. Draw a straight line through the plotted points.