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Sketch a graph of the linear equation. y = – 2x + 2 4- -5 -4 -3 -2 -1 --1 5 -2 -3

Sketch a graph of the linear equation. y = – 2x + 2 4- -5 -4 -3 -2 -1 --1 5 -2 -3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 15E
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### Plotting a Linear Equation #### Task: Sketch a graph of the linear equation: \[ y = -2x + 2 \] #### Explanation of the Graph: The provided graph is a coordinate plane with both x and y axes. The x-axis (horizontal) and y-axis (vertical) are labeled with numbers from -5 to 5. The graph has a grid with each line representing a single unit. ##### Steps to Plot the Equation: 1. **Find the y-intercept**: - The y-intercept is the point where the line crosses the y-axis. - For the equation \( y = -2x + 2 \), the y-intercept is 2. Plot this point on the y-axis at (0, 2). 2. **Use the Slope**: - The slope of the line is -2, which means for every 1 unit you move to the right on the x-axis, you move 2 units down on the y-axis. - From the y-intercept (0, 2), move 1 unit to the right (to x = 1) and 2 units down (to y = 0), arriving at the point (1, 0). Plot this point. 3. **Draw the Line**: - Connect the points (0, 2) and (1, 0) with a straight line. - Extend the line in both directions, maintaining the slope of -2, to complete the graph of the equation. This visual representation aids in understanding the relationship between the variables x and y as defined by the equation \( y = -2x + 2 \). The negative slope indicates that as x increases, y decreases.
Transcribed Image Text:### Plotting a Linear Equation #### Task: Sketch a graph of the linear equation: \[ y = -2x + 2 \] #### Explanation of the Graph: The provided graph is a coordinate plane with both x and y axes. The x-axis (horizontal) and y-axis (vertical) are labeled with numbers from -5 to 5. The graph has a grid with each line representing a single unit. ##### Steps to Plot the Equation: 1. **Find the y-intercept**: - The y-intercept is the point where the line crosses the y-axis. - For the equation \( y = -2x + 2 \), the y-intercept is 2. Plot this point on the y-axis at (0, 2). 2. **Use the Slope**: - The slope of the line is -2, which means for every 1 unit you move to the right on the x-axis, you move 2 units down on the y-axis. - From the y-intercept (0, 2), move 1 unit to the right (to x = 1) and 2 units down (to y = 0), arriving at the point (1, 0). Plot this point. 3. **Draw the Line**: - Connect the points (0, 2) and (1, 0) with a straight line. - Extend the line in both directions, maintaining the slope of -2, to complete the graph of the equation. This visual representation aids in understanding the relationship between the variables x and y as defined by the equation \( y = -2x + 2 \). The negative slope indicates that as x increases, y decreases.
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