Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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].
### 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].
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
