graph the line.\n$y = -2x - 4$

graph the line.\n$y = -2x - 4$

graph the line.\n$y = -2x - 4$

Answer

Explanation:

Step1: Identify the 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=-2x - 4), the y - intercept (b=-4). This means the line crosses the y - axis at the point ((0,-4)). We can plot this point on the coordinate plane.

Step2: Determine the slope

The slope (m=-2), which can be written as (\frac{-2}{1}) (or (\frac{2}{-1})). The slope represents the rise over run. Starting from the y - intercept ((0,-4)), if we use the slope (\frac{-2}{1}), we go down 2 units (because the numerator is - 2) and then 1 unit to the right (because the denominator is 1). This gives us the point ((0 + 1,-4-2)=(1,-6)). Alternatively, if we use (\frac{2}{-1}), we go up 2 units and 1 unit to the left, getting the point ((0 - 1,-4 + 2)=(-1,-2)).

Step3: Draw the line

After plotting two or more points (such as ((0,-4)), ((1,-6)), and ((-1,-2))), we can draw a straight line passing through these points. The line should extend infinitely in both directions.

Answer:

To graph (y = - 2x-4):

  1. Plot the y - intercept ((0,-4)).
  2. Use the slope (m=-2) to find another point (e.g., from ((0,-4)), move down 2 and right 1 to get ((1,-6)) or up 2 and left 1 to get ((-1,-2))).
  3. Draw a straight line through the plotted points.