Question

graph the line.
y = -x - 1

Explanation:

Step1: Identify slope and y-intercept

The equation \( y = -x - 1 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=- 1\) and \( b=-1\).

Step2: Plot the y - intercept

The y - intercept \( b = - 1\), so we plot the point \( (0,-1) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m=-1=\frac{-1}{1}\). From the point \( (0, - 1) \), we move down 1 unit (because the numerator of the slope is - 1) and right 1 unit (because the denominator of the slope is 1), or up 1 unit and left 1 unit. Moving down 1 and right 1 from \( (0,-1) \) gives us the point \( (1,-2) \). Moving up 1 and left 1 from \( (0,-1) \) gives us the point \( (-1,0) \).

Step4: Draw the line

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

Answer:

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

1. Plot the y - intercept at \( (0,-1) \).
2. Use the slope \( m = - 1\) to find additional points (e.g., \( (1,-2) \), \( (-1,0) \)).
3. Draw a straight line through these points. The line will have a negative slope, crossing the y - axis at \( (0,-1) \), passing through points like \( (-1,0) \) and \( (1,-2) \) etc. (The actual graph is a straight line with slope - 1 and y - intercept - 1 on the given coordinate plane.)