Question

graph the inequality in the coordinate plane. y < -3

Explanation:

Step1: Identify the boundary line

The inequality is \( y < -3 \). First, consider the equation \( y = -3 \). This is a horizontal line parallel to the x - axis, passing through the point \((x, - 3)\) for all \( x \). Since the inequality is \( y < -3 \) (not \( y\leq - 3\)), the boundary line should be a dashed line.

Step2: Determine the region to shade

We need to find the region where \( y \) - values are less than - 3. For a horizontal line \( y = k \), the region \( y < k \) is the area below the line. So, we shade the region below the dashed line \( y=-3\).

To graph it:

1. Draw a dashed horizontal line through \( y = - 3 \) (because the inequality is strict, \( y

eq - 3\)).

1. Shade the area below this dashed line. All points in this shaded region will satisfy the inequality \( y < - 3\).

Answer:

To graph \( y < - 3 \):

1. Draw a dashed horizontal line at \( y=-3\) (parallel to the x - axis, passing through \((x, - 3)\) for all \( x\)).
2. Shade the region below this dashed line (where all points have \( y\) - coordinates less than - 3).