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,...
Related questions
Question
![**Instruction: Sketch the Graph of the Equation**
Equation: \(-4x + 5y = 20\)
**Explanation:**
To graph the equation \(-4x + 5y = 20\), you can rearrange it into slope-intercept form \(y = mx + b\).
1. Rearrange the equation:
\[
5y = 4x + 20
\]
\[
y = \frac{4}{5}x + 4
\]
*The graph can be drawn on a coordinate plane:*
- **Axes**: The graph shows a typical Cartesian coordinate plane with horizontal \(x\)-axis and vertical \(y\)-axis, both marked with arrows indicating positive directions.
- **Grid**: The background consists of a grid to aid in plotting points accurately.
**Steps for Sketching:**
1. **Y-intercept**: The equation \(y = \frac{4}{5}x + 4\) shows that the y-intercept, where the line crosses the y-axis, is at \(y = 4\). Plot the point \( (0, 4) \).
2. **Slope**: The slope of the line \( \frac{4}{5} \) indicates that for every 5 units increase in \(x\), \(y\) increases by 4 units. From the y-intercept \( (0, 4) \), move 5 units to the right and 4 units up to plot the next point.
3. **Draw the Line**: Connect these points with a straight line to represent the equation.
This visual representation highlights how the linear equation can be plotted on a coordinate plane through understanding its slope and intercept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5df5842e-eea8-4ec3-8ea8-c27cad8d62e1%2Fb49eee34-8348-44bf-a404-ff2d537b9031%2F31koybu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction: Sketch the Graph of the Equation**
Equation: \(-4x + 5y = 20\)
**Explanation:**
To graph the equation \(-4x + 5y = 20\), you can rearrange it into slope-intercept form \(y = mx + b\).
1. Rearrange the equation:
\[
5y = 4x + 20
\]
\[
y = \frac{4}{5}x + 4
\]
*The graph can be drawn on a coordinate plane:*
- **Axes**: The graph shows a typical Cartesian coordinate plane with horizontal \(x\)-axis and vertical \(y\)-axis, both marked with arrows indicating positive directions.
- **Grid**: The background consists of a grid to aid in plotting points accurately.
**Steps for Sketching:**
1. **Y-intercept**: The equation \(y = \frac{4}{5}x + 4\) shows that the y-intercept, where the line crosses the y-axis, is at \(y = 4\). Plot the point \( (0, 4) \).
2. **Slope**: The slope of the line \( \frac{4}{5} \) indicates that for every 5 units increase in \(x\), \(y\) increases by 4 units. From the y-intercept \( (0, 4) \), move 5 units to the right and 4 units up to plot the next point.
3. **Draw the Line**: Connect these points with a straight line to represent the equation.
This visual representation highlights how the linear equation can be plotted on a coordinate plane through understanding its slope and intercept.
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