At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To graph the linear inequality [tex]\( 6x + 2y > -10 \)[/tex], we will follow these steps:
### Step 1: Rewrite the Inequality in Slope-Intercept Form
The inequality [tex]\( 6x + 2y > -10 \)[/tex] can be rewritten in slope-intercept form [tex]\( y = mx + b \)[/tex] by isolating [tex]\( y \)[/tex]:
1. Subtract [tex]\( 6x \)[/tex] from both sides:
[tex]\[ 2y > -6x - 10 \][/tex]
2. Divide every term by 2:
[tex]\[ y > -3x - 5 \][/tex]
### Step 2: Graph the Boundary Line
The boundary of the inequality [tex]\( y > -3x - 5 \)[/tex] is the line [tex]\( y = -3x - 5 \)[/tex]. This line is not included in the solution set because the inequality is strict (i.e., [tex]\( > \)[/tex] and not [tex]\( \geq \)[/tex]). Therefore, we should draw this line as a dashed line.
1. Identify the y-intercept ([tex]\( b \)[/tex]):
[tex]\[ y = -3x - 5 \implies b = -5 \][/tex]
2. Identify the slope ([tex]\( m \)[/tex]):
[tex]\[ y = -3x - 5 \implies m = -3 \][/tex]
3. Plot the y-intercept ([tex]\( 0, -5 \)[/tex]).
4. Use the slope to plot another point. The slope of -3 means you go down 3 units for every 1 unit you go to the right. Starting from [tex]\((0, -5)\)[/tex]:
- Move 1 unit to the right to [tex]\((1, -5)\)[/tex].
- Move down 3 units to [tex]\((1, -8)\)[/tex].
5. Draw a dashed line through these points to represent the boundary line.
### Step 3: Shade the Appropriate Region
Since the inequality is [tex]\( y > -3x - 5 \)[/tex]:
1. Identify that the region above the line represents [tex]\( y > -3x - 5 \)[/tex].
2. Shade the entire region above the dashed line, indicating all points in this area satisfy the inequality.
### Summary
The graph of the linear inequality [tex]\( 6x + 2y > -10 \)[/tex] consists of:
- A dashed line for the equation [tex]\( y = -3x - 5 \)[/tex], showing that points on the line are not included in the solution.
- Shading the region above the dashed line, since we are interested in the values [tex]\( y \)[/tex] greater than [tex]\( -3x - 5 \)[/tex].
By following these steps, you can accurately graph the linear inequality on a coordinate plane.
### Step 1: Rewrite the Inequality in Slope-Intercept Form
The inequality [tex]\( 6x + 2y > -10 \)[/tex] can be rewritten in slope-intercept form [tex]\( y = mx + b \)[/tex] by isolating [tex]\( y \)[/tex]:
1. Subtract [tex]\( 6x \)[/tex] from both sides:
[tex]\[ 2y > -6x - 10 \][/tex]
2. Divide every term by 2:
[tex]\[ y > -3x - 5 \][/tex]
### Step 2: Graph the Boundary Line
The boundary of the inequality [tex]\( y > -3x - 5 \)[/tex] is the line [tex]\( y = -3x - 5 \)[/tex]. This line is not included in the solution set because the inequality is strict (i.e., [tex]\( > \)[/tex] and not [tex]\( \geq \)[/tex]). Therefore, we should draw this line as a dashed line.
1. Identify the y-intercept ([tex]\( b \)[/tex]):
[tex]\[ y = -3x - 5 \implies b = -5 \][/tex]
2. Identify the slope ([tex]\( m \)[/tex]):
[tex]\[ y = -3x - 5 \implies m = -3 \][/tex]
3. Plot the y-intercept ([tex]\( 0, -5 \)[/tex]).
4. Use the slope to plot another point. The slope of -3 means you go down 3 units for every 1 unit you go to the right. Starting from [tex]\((0, -5)\)[/tex]:
- Move 1 unit to the right to [tex]\((1, -5)\)[/tex].
- Move down 3 units to [tex]\((1, -8)\)[/tex].
5. Draw a dashed line through these points to represent the boundary line.
### Step 3: Shade the Appropriate Region
Since the inequality is [tex]\( y > -3x - 5 \)[/tex]:
1. Identify that the region above the line represents [tex]\( y > -3x - 5 \)[/tex].
2. Shade the entire region above the dashed line, indicating all points in this area satisfy the inequality.
### Summary
The graph of the linear inequality [tex]\( 6x + 2y > -10 \)[/tex] consists of:
- A dashed line for the equation [tex]\( y = -3x - 5 \)[/tex], showing that points on the line are not included in the solution.
- Shading the region above the dashed line, since we are interested in the values [tex]\( y \)[/tex] greater than [tex]\( -3x - 5 \)[/tex].
By following these steps, you can accurately graph the linear inequality on a coordinate plane.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.