Question

graph the inequality.

$y > -5x - 2$

Explanation:

Step1: Identify the boundary line

The inequality is \( y > -5x - 2 \). First, consider the equation of the boundary line, which is \( y = -5x - 2 \). This is a linear equation in slope - intercept form (\( y=mx + b \)), where the slope \( m=-5 \) and the y - intercept \( b = - 2 \). To graph the boundary line, we start by plotting the y - intercept. The y - intercept is the point where \( x = 0 \), so when \( x = 0 \), \( y=-2 \). Then, using the slope, which is \( \frac{\text{rise}}{\text{run}}=\frac{- 5}{1} \), from the point \( (0,-2) \), we can go down 5 units and right 1 unit (or up 5 units and left 1 unit) to find another point on the line. Since the inequality is \( y > -5x - 2 \) (not \( y\geq - 5x - 2 \)), 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 \( y>-5x - 2 \):
\( 0>-5(0)-2 \)
\( 0> - 2 \), which is a true statement. So, we shade the region that contains the point \( (0,0) \), which is the region above the dashed line \( y=-5x - 2 \).

Answer:

1. Draw a dashed line with slope - 5 and y - intercept - 2 (passing through \( (0,-2) \) and other points found using the slope).
2. Shade the region above the dashed line (the region that contains the point \( (0,0) \)).