Question

which description of the graph of the linear inequality y ≥ 3x - 8 is correct?

• the graph will be a dashed line with a y - intercept of negative eight and a slope of three. the graph will be shaded below the line.
• the graph will be a solid line with a y - intercept of three and a slope of negative eight. the graph will be shaded above the line.
• the graph will be a solid line with a y - intercept of three and a slope of negative eight. the graph will be shaded below the line.
• the graph will be a dashed line with a y - intercept of negative eight and a slope of three. the graph will be shaded above the line.

Explanation:

Step1: Analyze the inequality form

The given inequality is \( y \geq 3x - 8 \). The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For the line \( y = 3x-8 \), the slope \( m = 3 \) and the y - intercept \( b=- 8 \) (negative eight).
Since the inequality is \( y\geq3x - 8 \), the line will be a solid line (because the inequality is "greater than or equal to", which includes the line itself).

Step2: Determine the shading region

To determine the shading, we can use a test point. A common test point is \( (0,0) \). Substitute \( x = 0 \) and \( y = 0 \) into the inequality: \( 0\geq3(0)-8\), which simplifies to \( 0\geq - 8 \). This is a true statement. So the region that includes the point \( (0,0) \) (above the line \( y = 3x-8 \)) should be shaded.

Answer:

The graph will be a solid line with a y - intercept of negative eight and a slope of three. The graph will be shaded above the line. (Assuming the last option in the original problem has this description. Since the original options are a bit garbled, but based on the analysis of \( y\geq3x - 8 \), the correct description should match the line type (solid), slope (3), y - intercept (-8), and shading (above the line).)