Graph: y = 4 To find three ordered-pair solutions of this equation to plot, we will select three values for x and use 4 for y each time. The given equation requires that y = 4. We can write the equation in general form as 0x + y = 4. Since the coefficient of x is 0, the numbers chosen for x have no effect on y. The value of y is always 4. For example, if X = 2, we have Ox + y = 4 This is the given equation, y = 4, written in standard (general) form. 0(2) + y = Substitute 2 for x. y = Simplify the left side. One solution is (2, 4). To find two more solutions, we choose x = 0 and x = -3. For any x-value, the y-value is always 4, so we enter (0, 4) and (-3, 4) in the table. If we plot the ordered pairs and draw a straight line through the points, the result is a horizontal line. The y-intercept is (0, 4) and there is no x-intercept. y y = 4 y (х, у) (-3, 4) (0, 4) (2, 4) (2, O) 4 y = 4 4 (0, (-3, O) -3 4 -3 -2 2 Choose any number for Each value of y must be 4. х. -2 Graph: y = -5
Graph: y = 4 To find three ordered-pair solutions of this equation to plot, we will select three values for x and use 4 for y each time. The given equation requires that y = 4. We can write the equation in general form as 0x + y = 4. Since the coefficient of x is 0, the numbers chosen for x have no effect on y. The value of y is always 4. For example, if X = 2, we have Ox + y = 4 This is the given equation, y = 4, written in standard (general) form. 0(2) + y = Substitute 2 for x. y = Simplify the left side. One solution is (2, 4). To find two more solutions, we choose x = 0 and x = -3. For any x-value, the y-value is always 4, so we enter (0, 4) and (-3, 4) in the table. If we plot the ordered pairs and draw a straight line through the points, the result is a horizontal line. The y-intercept is (0, 4) and there is no x-intercept. y y = 4 y (х, у) (-3, 4) (0, 4) (2, 4) (2, O) 4 y = 4 4 (0, (-3, O) -3 4 -3 -2 2 Choose any number for Each value of y must be 4. х. -2 Graph: y = -5
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:### Understanding the Graph of a Linear Equation
**Objective:**
Learn how to graph the linear equation \( y = -5 \) using a graphing tool.
**Graph:**
#### Equation: \( y = -5 \)
**Graphical Representation:**
- This equation represents a horizontal line where the y-coordinate is constantly \(-5\) for all values of \(x\).
**Graphical Interface and Tools:**
1. **Graph Display:**
- The graphing area shows a Cartesian coordinate system with equal intervals for both \(x\) and \(y\) axes.
- The \(x\)-axis and \(y\)-axis are both labeled from \(-10\) to \(10\) with gridlines to assist in plotting points.
2. **Tools Available on the Left Toolbar:**
- **Pointer Tool:** Used for selecting objects on the graph.
- **Line Tool:** Used for drawing straight lines.
- **Circle Tool:** Used for drawing circles.
- **Parabola Tool:** Used for drawing parabolic curves.
- **Point Tool:** Used for plotting and marking specific points.
- **No Solution Tool:** Marks equations or graphs with no solution.
3. **Graph Layers Panel (Right Side):**
- This panel helps in managing the different objects and elements on the graph.
- The description states: "After you add an object to the graph you can use Graph Layers to view and edit its properties."
4. **Actions Panel (Right Side):**
- **Clear All:** Clear all objects on the graph.
- **Delete:** Remove selected objects.
- **Fill:** Used for coloring the objects.
5. **Help Button (Bottom Left Corner):**
- Provides assistance and additional information about using the graphing tool.
**Plotting the Equation \( y = -5 \):**
- Locate the y-intercept at \( y = -5 \).
- Draw a horizontal line through the point where \( y = -5 \) across the entire span of the graph.
- Ensure the line is parallel to the x-axis to accurately represent the equation.
This graphing tool, provided by WebAssign, ensures a comprehensive and interactive experience to enhance understanding and visualization of mathematical concepts.
![### Graphing the Equation \( y = 4 \)
When graphing the equation \( y = 4 \), we need to find three ordered-pair solutions to plot. For consistency, we will choose different values for \( x \) and use \( y = 4 \) for each one.
#### Step-by-Step Solution:
1. The given equation is \( y = 4 \).
2. **General Form of the Equation:**
We can rewrite the equation in general form as \( 0x + y = 4 \).
Since the coefficient of \( x \) is 0, the \( x \)-values do not affect the \( y \)-values. Therefore, for any chosen \( x \), \( y \) will always be 4.
3. **Example Calculation:**
For \( x = 2 \):
\[
0(2) + y = 4 \quad \text{(Substitute \( 2 \) for \( x \))}
\]
\[
y = 4 \quad \text{(Simplify the left side)}
\]
This results in the ordered-pair \((2, 4)\).
4. **Finding More Solutions:**
To find two more solutions, we choose \( x = 0 \) and \( x = -3 \). For any \( x \)-value, the \( y \)-value must always be 4.
Thus, the ordered pairs are:
\[
(0, 4) \quad \text{and} \quad (-3, 4)
\]
5. **Summary of Ordered Pairs:**
\[
(2, 4), \quad (0, 4), \quad (-3, 4)
\]
6. **Plotting the Points:**
On a graph, plot the points \((2, 4)\), \((0, 4)\), and \((-3, 4)\). Draw a straight line through these points.
- The graph depicts a horizontal line at \( y = 4 \).
- The \( y \)-intercept is \( (0, 4) \).
- There is no \( x \)-intercept because the line never crosses the \( x \)-axis.
### Graph and Table Representation:
The table and graph below summarize the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46673039-9c26-4fb7-977e-77e5eaa45b18%2Fab0c6c74-8b11-42be-a542-ad5d8aef01d6%2Fk8pocrd_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing the Equation \( y = 4 \)
When graphing the equation \( y = 4 \), we need to find three ordered-pair solutions to plot. For consistency, we will choose different values for \( x \) and use \( y = 4 \) for each one.
#### Step-by-Step Solution:
1. The given equation is \( y = 4 \).
2. **General Form of the Equation:**
We can rewrite the equation in general form as \( 0x + y = 4 \).
Since the coefficient of \( x \) is 0, the \( x \)-values do not affect the \( y \)-values. Therefore, for any chosen \( x \), \( y \) will always be 4.
3. **Example Calculation:**
For \( x = 2 \):
\[
0(2) + y = 4 \quad \text{(Substitute \( 2 \) for \( x \))}
\]
\[
y = 4 \quad \text{(Simplify the left side)}
\]
This results in the ordered-pair \((2, 4)\).
4. **Finding More Solutions:**
To find two more solutions, we choose \( x = 0 \) and \( x = -3 \). For any \( x \)-value, the \( y \)-value must always be 4.
Thus, the ordered pairs are:
\[
(0, 4) \quad \text{and} \quad (-3, 4)
\]
5. **Summary of Ordered Pairs:**
\[
(2, 4), \quad (0, 4), \quad (-3, 4)
\]
6. **Plotting the Points:**
On a graph, plot the points \((2, 4)\), \((0, 4)\), and \((-3, 4)\). Draw a straight line through these points.
- The graph depicts a horizontal line at \( y = 4 \).
- The \( y \)-intercept is \( (0, 4) \).
- There is no \( x \)-intercept because the line never crosses the \( x \)-axis.
### Graph and Table Representation:
The table and graph below summarize the
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