graph the inequality on the axes below.\n$y > -3x - 4$

Explanation:

Step1: Graph the boundary line

The inequality is ( y > -3x - 4 ). First, consider the boundary line ( y = -3x - 4 ). This is a linear equation in slope - intercept form ( y=mx + b ), where the slope ( m=-3 ) and the y - intercept ( b = - 4 ). To graph the line, start by plotting the y - intercept. The y - intercept is at ( (0,-4) ). Then, use the slope to find another point. The slope ( m=\frac{\text{rise}}{\text{run}}=-3=\frac{-3}{1} ). From the point ( (0,-4) ), move down 3 units (because the rise is - 3) and 1 unit to the right (run is 1) to get the point ( (1,-7) ), or move up 3 units and 1 unit to the left to get the point ( (-1,-1) ). Since the inequality is ( y > -3x - 4 ) (not ( y\geq - 3x - 4 )), the boundary line should be a dashed line.

Step2: Determine the region to shade

To determine which side of the line to shade, we can use a test point. A common test point is ( (0,0) ) (as long as it is not on the boundary line). Substitute ( x = 0 ) and ( y = 0 ) into the inequality ( y>-3x - 4 ): ( 0>-3(0)-4 ) ( 0> - 4 ), which is a true statement. So, we shade the region that contains the point ( (0,0) ), which is the region above the dashed line ( y=-3x - 4 ).

Answer:

1. Draw a dashed line with slope - 3 and y - intercept - 4 (passing through points like ( (0,-4) ) and ( (1,-7) ) or ( (-1,-1) )).
2. Shade the region above the dashed line (the region that includes the point ( (0,0) )).