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

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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### 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.
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
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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