Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
### Graph the Line 3y - x = -6 Use the provided graph to plot the line described by the equation 3y - x = -6. Below is an explanation on how we can approach graphing this equation: 1. **Transform the Equation**: Rearrange the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. \[ 3y - x = -6 \\ \Rightarrow 3y = x - 6 \\ \Rightarrow y = \frac{1}{3}x - 2 \] Here, the slope (m) is \( \frac{1}{3} \) and the y-intercept (b) is -2. 2. **Plot the Y-Intercept**: Start by plotting the y-intercept on the graph. Here, the y-intercept is at (0, -2). Mark this point on the vertical axis. 3. **Use the Slope to Find Another Point**: The slope of \( \frac{1}{3} \) means that for every 1 unit we move horizontally to the right, we move up by \( \frac{1}{3} \) units. From the point (0, -2), move 3 units to the right and 1 unit up to find another point on the line, which is (3, -1). 4. **Draw the Line**: Using a ruler or a straight-edge tool, draw a line through the points (0, -2) and (3, -1) extending it in both directions. ### Graph Description: The graph displays a standard coordinate plane with x and y axes ranging from -5 to 5. - The horizontal axis (x-axis) is labeled from -5 to 5. - The vertical axis (y-axis) is labeled from -5 to 5. ### Tool Instructions: At the bottom of the graph interface, there are multiple tool options: - Line tool: Select to draw straight lines. - Parabola tool: Select to draw parabola shapes. - Angle tool: Select to draw angles. - Circle tool: Select to draw circles. - Clear All button: Use to clear the graph and start over. Ensure you use the straight line tool to plot the line \( y = \frac{1
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Transcribed Image Text:### Graph the Line 3y - x = -6 Use the provided graph to plot the line described by the equation 3y - x = -6. Below is an explanation on how we can approach graphing this equation: 1. **Transform the Equation**: Rearrange the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. \[ 3y - x = -6 \\ \Rightarrow 3y = x - 6 \\ \Rightarrow y = \frac{1}{3}x - 2 \] Here, the slope (m) is \( \frac{1}{3} \) and the y-intercept (b) is -2. 2. **Plot the Y-Intercept**: Start by plotting the y-intercept on the graph. Here, the y-intercept is at (0, -2). Mark this point on the vertical axis. 3. **Use the Slope to Find Another Point**: The slope of \( \frac{1}{3} \) means that for every 1 unit we move horizontally to the right, we move up by \( \frac{1}{3} \) units. From the point (0, -2), move 3 units to the right and 1 unit up to find another point on the line, which is (3, -1). 4. **Draw the Line**: Using a ruler or a straight-edge tool, draw a line through the points (0, -2) and (3, -1) extending it in both directions. ### Graph Description: The graph displays a standard coordinate plane with x and y axes ranging from -5 to 5. - The horizontal axis (x-axis) is labeled from -5 to 5. - The vertical axis (y-axis) is labeled from -5 to 5. ### Tool Instructions: At the bottom of the graph interface, there are multiple tool options: - Line tool: Select to draw straight lines. - Parabola tool: Select to draw parabola shapes. - Angle tool: Select to draw angles. - Circle tool: Select to draw circles. - Clear All button: Use to clear the graph and start over. Ensure you use the straight line tool to plot the line \( y = \frac{1
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