y3D-2x-4

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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## Graphing Linear Equations

### Objective:
Learn how to graph the linear equation \( y = -2x - 4 \) on a coordinate plane.

### Equation Provided:
\[ y = -2x - 4 \]

### Graph Explanation:
1. **Coordinate Plane**:
   - The graph is plotted on a standard Cartesian coordinate system.
   - The x-axis ranges from -8 to 8.
   - The y-axis ranges from -8 to 8.
   - Grid lines are present for each unit on both axes.

2. **Plot Points**:
   - The line intersects the y-axis at \( y = -4 \). This is the y-intercept.
   - Another point on the line can be found by using the slope \( m = -2 \). For instance, when \( x = 2 \), \( y = -2(2) - 4 = -8 \).

3. **Drawing the Line**:
   - A straight line is drawn through the points \((0, -4)\) and \((1, -6)\) to represent the linear equation.
   - The line extends in both directions, passing through and beyond these plotted points, demonstrating the continuous nature of linear equations.

4. **Check Button**:
   - There is a “Check” button below the graph, likely used to verify the accuracy of the drawn line against the provided equation.
  
### Detailed Steps to Plot the Line:
1. **Find the y-intercept**:
   - Substitute \( x = 0 \) in the equation \( y = -2x - 4 \):
     \[ y = -2(0) - 4 \]
     \[ y = -4 \]
   - Plot the point \((0, -4)\) on the graph.

2. **Use the Slope**:
   - The slope \( m = -2 \) indicates that for every 1 unit increase in \( x \), \( y \) decreases by 2 units.
   - Starting from \((0, -4)\), move 1 unit to the right to \( x = 1 \) and 2 units down to \( y = -6 \). Plot the point \((1, -6)\).

3. **Draw the Line**:
   - Connect these points with a straight line, extending it in both directions.

4. **Verify Accuracy** (if
Transcribed Image Text:## Graphing Linear Equations ### Objective: Learn how to graph the linear equation \( y = -2x - 4 \) on a coordinate plane. ### Equation Provided: \[ y = -2x - 4 \] ### Graph Explanation: 1. **Coordinate Plane**: - The graph is plotted on a standard Cartesian coordinate system. - The x-axis ranges from -8 to 8. - The y-axis ranges from -8 to 8. - Grid lines are present for each unit on both axes. 2. **Plot Points**: - The line intersects the y-axis at \( y = -4 \). This is the y-intercept. - Another point on the line can be found by using the slope \( m = -2 \). For instance, when \( x = 2 \), \( y = -2(2) - 4 = -8 \). 3. **Drawing the Line**: - A straight line is drawn through the points \((0, -4)\) and \((1, -6)\) to represent the linear equation. - The line extends in both directions, passing through and beyond these plotted points, demonstrating the continuous nature of linear equations. 4. **Check Button**: - There is a “Check” button below the graph, likely used to verify the accuracy of the drawn line against the provided equation. ### Detailed Steps to Plot the Line: 1. **Find the y-intercept**: - Substitute \( x = 0 \) in the equation \( y = -2x - 4 \): \[ y = -2(0) - 4 \] \[ y = -4 \] - Plot the point \((0, -4)\) on the graph. 2. **Use the Slope**: - The slope \( m = -2 \) indicates that for every 1 unit increase in \( x \), \( y \) decreases by 2 units. - Starting from \((0, -4)\), move 1 unit to the right to \( x = 1 \) and 2 units down to \( y = -6 \). Plot the point \((1, -6)\). 3. **Draw the Line**: - Connect these points with a straight line, extending it in both directions. 4. **Verify Accuracy** (if
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