Question

y > -3x - 8

Explanation:

Step1: Identify the type of line

The inequality is \( y > -3x - 8 \). Since the inequality is "greater than" (not "greater than or equal to"), the boundary line will be dashed. The slope of the line \( y = -3x - 8 \) is \( -3 \) and the y - intercept is \( -8 \).

Step2: Graph the boundary line

• Plot the y - intercept: The y - intercept is \( b=-8 \), so we plot the point \( (0, - 8) \).
• Use the slope to find another point: The slope \( m=-3=\frac{-3}{1} \). From the point \( (0, - 8) \), we move down 3 units (because the numerator of the slope is - 3) and 1 unit to the right (because the denominator of the slope is 1) to get the point \( (1,-11) \), or we can move up 3 units and 1 unit to the left to get the point \( (- 1,-5) \). Draw a dashed line through these points (since the inequality is strict, \( y>-3x - 8 \), not \( y\geq-3x - 8 \)).

Step3: 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 line). Substitute \( x = 0 \) and \( y = 0 \) into the inequality:
\( 0>-3(0)-8 \)
\( 0> - 8 \)
This statement is true. So we shade the region that contains the point \( (0,0) \).

Answer:

1. Draw a dashed line with slope - 3 and y - intercept - 8 (equation \( y=-3x - 8 \)).
2. Shade the region above the dashed line (the region that contains the point \( (0,0) \)).