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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![## 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61c70154-6dcc-4ad1-b23f-82f068f0fd01%2F2424607d-5960-41dc-b9fa-91351227e4c8%2Fvjoyo0e.jpeg&w=3840&q=75)
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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