Question

graph the inequality.
$y < x - 5$

Explanation:

Step1: Graph the boundary line

The inequality is \( y < x - 5 \). First, graph the line \( y = x - 5 \). This is a linear equation in slope - intercept form (\( y=mx + b \)) where the slope \( m = 1 \) and the y - intercept \( b=- 5 \). Since the inequality is \( y

Step2: Determine the shading region

To determine which side of the line to shade, we can use a test point. A common test point is the origin \((0,0)\) (as long as it is not on the boundary line). Substitute \( x = 0 \) and \( y = 0 \) into the inequality \( y\( 0<0 - 5 \)
\( 0<-5 \), which is false. So the origin is not in the solution set. We shade the region that does not include the origin. Since the slope of the line \( y=x - 5 \) is positive, the line goes up from left to right. The solution set (the region to shade) is below the dashed line \( y=x - 5 \).

Answer:

To graph \( y < x-5 \):

1. Draw a dashed line for \( y=x - 5 \) (slope = 1, y - intercept=-5).
2. Shade the region below the dashed line (test point \((0,0)\) does not satisfy \( y < x - 5 \), so shade the side opposite to the origin relative to the line \( y=x - 5 \)).