Question

graph the linear inequality shown below on the provided graph.
$y > -3x + 8$

Explanation:

Step1: Identify the line type

The inequality is \( y > -3x + 8 \), which is a strict inequality (\(>\)), so we use a dashed line (since the points on the line \( y = -3x + 8 \) are not included in the solution set).

Step2: Find two points on the line \( y = -3x + 8 \)

• When \( x = 0 \), \( y = -3(0)+8 = 8 \), so the point is \( (0, 8) \).
• When \( x = 1 \), \( y = -3(1)+8 = 5 \), so the point is \( (1, 5) \).

Plot these two points and draw a dashed line through them.

Step3: Determine the shaded region

To find which side of the line to shade, we can test a point not on the line. Let's use the origin \( (0, 0) \):
Substitute \( x = 0 \), \( y = 0 \) into the inequality: \( 0 > -3(0)+8 \) → \( 0 > 8 \), which is false. So we shade the region that does not include the origin, i.e., the region above the dashed line \( y = -3x + 8 \).

(Note: Since this is a graphing problem, the final answer is the graph with the dashed line \( y = -3x + 8 \) and the region above it shaded. The steps above describe how to construct that graph.)

Answer:

Step1: Identify the line type

The inequality is \( y > -3x + 8 \), which is a strict inequality (\(>\)), so we use a dashed line (since the points on the line \( y = -3x + 8 \) are not included in the solution set).

Step2: Find two points on the line \( y = -3x + 8 \)

• When \( x = 0 \), \( y = -3(0)+8 = 8 \), so the point is \( (0, 8) \).
• When \( x = 1 \), \( y = -3(1)+8 = 5 \), so the point is \( (1, 5) \).

Plot these two points and draw a dashed line through them.

Step3: Determine the shaded region

To find which side of the line to shade, we can test a point not on the line. Let's use the origin \( (0, 0) \):
Substitute \( x = 0 \), \( y = 0 \) into the inequality: \( 0 > -3(0)+8 \) → \( 0 > 8 \), which is false. So we shade the region that does not include the origin, i.e., the region above the dashed line \( y = -3x + 8 \).

(Note: Since this is a graphing problem, the final answer is the graph with the dashed line \( y = -3x + 8 \) and the region above it shaded. The steps above describe how to construct that graph.)