Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.7: Graphing Linear Inequalities
Problem 7OE
Related questions
Question
![**Plotting an Inequality on a Coordinate Plane: y > (5/3)x - 3**
**Instructions:**
To graph the inequality \( y > \frac{5}{3}x - 3 \) follow these steps. Take special note of whether to use a solid or dashed line, which depends on the inequality sign.
**Step-by-step Guide:**
1. **Graph the Line:**
- Begin by graphing the line \( y = \frac{5}{3}x - 3 \). This is the boundary line.
- Since the inequality \( y > \frac{5}{3}x - 3 \) does not include equality (it is strictly greater than), use a dashed line to indicate that points on the line itself are not included in the solution.
2. **Identify Key Points:**
- Plot the y-intercept. The y-intercept is the point where x equals 0.
\[ y = \frac{5}{3}(0) - 3 = -3 \]
So, the y-intercept is (0, -3).
- Next, use the slope \( \frac{5}{3} \) to find another point. The slope tells you that for every 3 units you move to the right (positive x-direction), you move 5 units up (positive y-direction).
3. **Example Calculations for Points:**
- Start from the y-intercept (0, -3). Move 3 units to the right which takes you to (3, -3).
- From (3, -3), move 5 units up which brings the point to (3, 2). These points help to draw the dashed line.
4. **Shade the Region:**
- Since the inequality is \( y > \frac{5}{3}x - 3 \), shade the region above the dashed line. This represents all the points where y is greater than \( \frac{5}{3}x - 3 \).
**Graph Explanation:**
- **Axes:**
The graph has a horizontal x-axis and a vertical y-axis, with both axes marked from -5 to 5 in increments of 1.
- **Gridlines:**
Gridlines are present to assist in plotting points accurately.
- **Key Labels:**
- The key points labeled are: (-5, 0);](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faafb6581-a416-4343-8433-9ce87f761f9f%2F9ec65b9f-b19b-4b6b-8ee4-fd242b553fec%2F41n4cmaj_processed.png&w=3840&q=75)
Transcribed Image Text:**Plotting an Inequality on a Coordinate Plane: y > (5/3)x - 3**
**Instructions:**
To graph the inequality \( y > \frac{5}{3}x - 3 \) follow these steps. Take special note of whether to use a solid or dashed line, which depends on the inequality sign.
**Step-by-step Guide:**
1. **Graph the Line:**
- Begin by graphing the line \( y = \frac{5}{3}x - 3 \). This is the boundary line.
- Since the inequality \( y > \frac{5}{3}x - 3 \) does not include equality (it is strictly greater than), use a dashed line to indicate that points on the line itself are not included in the solution.
2. **Identify Key Points:**
- Plot the y-intercept. The y-intercept is the point where x equals 0.
\[ y = \frac{5}{3}(0) - 3 = -3 \]
So, the y-intercept is (0, -3).
- Next, use the slope \( \frac{5}{3} \) to find another point. The slope tells you that for every 3 units you move to the right (positive x-direction), you move 5 units up (positive y-direction).
3. **Example Calculations for Points:**
- Start from the y-intercept (0, -3). Move 3 units to the right which takes you to (3, -3).
- From (3, -3), move 5 units up which brings the point to (3, 2). These points help to draw the dashed line.
4. **Shade the Region:**
- Since the inequality is \( y > \frac{5}{3}x - 3 \), shade the region above the dashed line. This represents all the points where y is greater than \( \frac{5}{3}x - 3 \).
**Graph Explanation:**
- **Axes:**
The graph has a horizontal x-axis and a vertical y-axis, with both axes marked from -5 to 5 in increments of 1.
- **Gridlines:**
Gridlines are present to assist in plotting points accurately.
- **Key Labels:**
- The key points labeled are: (-5, 0);
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