To graph the linear inequality [tex]\( y > 3x - 8 \)[/tex], let's analyze the components step by step:
1. Slope and y-intercept:
- The inequality [tex]\( y > 3x - 8 \)[/tex] can be broken down into the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- Here, [tex]\( m = 3 \)[/tex] (slope) and [tex]\( b = -8 \)[/tex] (y-intercept).
2. Type of line:
- An important aspect to note is whether the line will be solid or dashed.
- Since the inequality is strict ( [tex]\( y > \)[/tex] rather than [tex]\( y \geq \)[/tex]), it means the points on the line [tex]\( y = 3x - 8 \)[/tex] are not included in the solution. Therefore, the line will be dashed.
3. Shading the region:
- The inequality [tex]\( y > 3x - 8 \)[/tex] implies that we need the region where the y-values are greater than the corresponding values on the line [tex]\( y = 3x - 8 \)[/tex].
- This means we will shade the region above the dashed line.
Putting this all together, the correct description of the graph for the inequality [tex]\( y > 3x - 8 \)[/tex] is:
- A dashed line with a [tex]\( y \)[/tex]-intercept of [tex]\(-8\)[/tex] and a slope of [tex]\(3\)[/tex].
- The region above the line will be shaded.
Therefore, the correct choice is:
- The graph will be a dashed line with a [tex]\( y \)[/tex]-intercept of negative eight and a slope of three. The graph will be shaded above the line.
