Graph the line. 1 . リーーX+3 4 y%3D

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**

### Instructions:
Graph the line represented by the following equation:
\[ y = -\frac{1}{4}x + 3 \]

### Steps to Graph the Line:
1. **Identify the y-intercept**: The y-intercept of the line is the point where the line crosses the y-axis. In the equation \( y = -\frac{1}{4}x + 3 \), the y-intercept is 3. This means the line will cross the y-axis at (0, 3).

2. **Determine the slope**: The slope of the line is represented by the coefficient of \( x \), which in this case is \(-\frac{1}{4}\). The slope indicates that for every 4 units you move to the right along the x-axis, you move 1 unit down along the y-axis (since the slope is negative).

3. **Plot the y-intercept**: Start by plotting the point (0, 3) on the graph.

4. **Use the slope to find another point**: From the y-intercept (0, 3), move 4 units to the right to (4, 3), then move 1 unit down to (4, 2). Thus, the second point is (4, 2).

5. **Draw the line**: Connect these two points with a straight line, extending the line across the graph.

### Details of the Graph:
- The x-axis and y-axis are labeled and numbered, spanning from -10 to 10.
- Both axes are marked in increments of 1.
- The grid lines help to visualize and accurately plot the points.

### Graph Interpretation:
Once the points (0, 3) and (4, 2) are plotted, drawing a straight line through these points will represent the line described by the equation \( y = -\frac{1}{4}x + 3 \). Ensure the line extends across the entire graph window for completeness.

### Practice:
After plotting the line, click the "Check" button to verify the accuracy of your graph. Adjust if necessary based on the feedback.

This exercise demonstrates the fundamental skills of interpreting and graphing linear equations, essential for understanding algebra and coordinate geometry.
Transcribed Image Text:**Graphing Linear Equations** ### Instructions: Graph the line represented by the following equation: \[ y = -\frac{1}{4}x + 3 \] ### Steps to Graph the Line: 1. **Identify the y-intercept**: The y-intercept of the line is the point where the line crosses the y-axis. In the equation \( y = -\frac{1}{4}x + 3 \), the y-intercept is 3. This means the line will cross the y-axis at (0, 3). 2. **Determine the slope**: The slope of the line is represented by the coefficient of \( x \), which in this case is \(-\frac{1}{4}\). The slope indicates that for every 4 units you move to the right along the x-axis, you move 1 unit down along the y-axis (since the slope is negative). 3. **Plot the y-intercept**: Start by plotting the point (0, 3) on the graph. 4. **Use the slope to find another point**: From the y-intercept (0, 3), move 4 units to the right to (4, 3), then move 1 unit down to (4, 2). Thus, the second point is (4, 2). 5. **Draw the line**: Connect these two points with a straight line, extending the line across the graph. ### Details of the Graph: - The x-axis and y-axis are labeled and numbered, spanning from -10 to 10. - Both axes are marked in increments of 1. - The grid lines help to visualize and accurately plot the points. ### Graph Interpretation: Once the points (0, 3) and (4, 2) are plotted, drawing a straight line through these points will represent the line described by the equation \( y = -\frac{1}{4}x + 3 \). Ensure the line extends across the entire graph window for completeness. ### Practice: After plotting the line, click the "Check" button to verify the accuracy of your graph. Adjust if necessary based on the feedback. This exercise demonstrates the fundamental skills of interpreting and graphing linear equations, essential for understanding algebra and coordinate geometry.
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