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Which description of the graph of the linear inequality [tex]y \ \textgreater \ 3x - 8[/tex] is correct?

A. 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 below the line.
B. The graph will be a solid line with a [tex]y[/tex]-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C. The graph will be a solid line with a [tex]y[/tex]-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D. 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.

Sagot :

GinnyAnswer
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.
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