Question

graph the line with the equation $y = -x - 3$.

Explanation:

Answer:

To graph \( y = -x - 3 \), follow these steps:

Step 1: Identify the slope and y-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For \( y=-x - 3 \), the slope \( m=- 1\) (which can be written as \( \frac{-1}{1}\)) and the y - intercept \( b=-3 \).

Step 2: Plot the y - intercept

The y - intercept is \( b = - 3 \), so we plot the point \( (0,-3) \) on the y - axis.

Step 3: Use the slope to find another point

The slope \( m=\frac{\text{rise}}{\text{run}}=-1=\frac{-1}{1} \). Starting from the point \( (0,-3) \), we move down 1 unit (because the rise is - 1) and then 1 unit to the right (because the run is 1). This gives us the point \( (1,-4) \). We can also move up 1 unit and left 1 unit from \( (0,-3) \) to get the point \( (- 1,-2) \) (since \( \frac{1}{-1}=-1\) as well).

Step 4: Draw the line

Draw a straight line through the points we have plotted (such as \( (0,-3) \), \( (1,-4) \), \( (-1,-2) \)) to represent the equation \( y=-x - 3 \) on the coordinate plane.

(Note: If we want to check with the given graph, the current blue dot at \( (1,3) \) is incorrect. The correct points should be around \( (0, - 3)\), \( (1,-4) \) etc. and the line passing through them.)