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Which description of the graph of the linear inequality [tex]y \geq 7x - 4[/tex] is correct?

A. The graph will be a dashed line with a y-intercept of -4 and a slope of 7. The graph will be shaded below the line.
B. The graph will be a solid line with a y-intercept of -4 and a slope of 7. The graph will be shaded above the line.
C. The graph will be a solid line with a y-intercept of 7 and a slope of -4. The graph will be shaded below the line.
D. The graph will be a dashed line with a y-intercept of 7 and a slope of -4. The graph will be shaded above the line.

Sagot :

GinnyAnsweridn
To solve the given problem accurately, let us analyze the linear inequality [tex]\( y \geq 7x - 4 \)[/tex].

### Step-by-Step Solution:

1. Identify the General Form:
The inequality [tex]\( y \geq 7x - 4 \)[/tex] can be compared to the standard form [tex]\( y \geq mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

2. Determine the Slope and Y-Intercept:
- Slope ([tex]\( m \)[/tex]): The coefficient of [tex]\( x \)[/tex] in the equation is [tex]\( 7 \)[/tex]. Therefore, the slope [tex]\( m = 7 \)[/tex].
- Y-Intercept ([tex]\( b \)[/tex]): The constant term is [tex]\(-4\)[/tex]. Thus, the y-intercept [tex]\( b = -4 \)[/tex].

3. Type of Line:
Since the inequality is [tex]\( \geq \)[/tex] (greater than or equal to), the line that represents [tex]\( y = 7x - 4 \)[/tex] will be solid. A solid line is used to indicate that points on the line itself are included in the solution set.

4. Shading the Graph:
The inequality [tex]\( y \geq 7x - 4 \)[/tex] indicates that we are looking for all values of [tex]\( y \)[/tex] that are greater than or equal to [tex]\( 7x - 4 \)[/tex]. Therefore, the region above the line [tex]\( y = 7x - 4 \)[/tex] will be shaded.

- The term "above" refers to the region on the graph where [tex]\( y \)[/tex] values are higher than the values on the line [tex]\( y = 7x - 4 \)[/tex].

### Final Description:

Using the correct values and interpretation, we define the characteristics of the correct graph:
- Line Type: Solid (because of [tex]\( \geq \)[/tex])
- Slope: 7
- Y-Intercept: -4
- Shaded Region: Above the line

After analyzing all the given answer choices, the correct description is:

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

Therefore, the correct choice is the second description, which corresponds to:

2. The graph will be a sold line weth a yirtercept of negative four and a slope of seven. The graph will be shaded atove the line.

This description accurately represents the graph of the inequality [tex]\( y \geq 7x - 4 \)[/tex].
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