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Graph the 5 -4 -3 SY - -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5+ 1 2 3 4 +5

Graph the 5 -4 -3 SY - -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5+ 1 2 3 4 +5

Algebra and Trigonometry (6th Edition)
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 the Line \(3y - 1x = -6\)** This image demonstrates how to graph the linear equation \(3y - 1x = -6\) on a coordinate plane. **Equation Breakdown:** 1. **Rearrange the equation:** - Start by solving for \(y\): - \(3y = x - 6\) - \(y = \frac{1}{3}x - 2\) 2. **Identify the slope and y-intercept:** - The equation \(y = \frac{1}{3}x - 2\) is in slope-intercept form \(y = mx + b\). - Slope \(m = \frac{1}{3}\) - Y-intercept \(b = -2\) **Graph Details:** - **Axes:** - The x-axis and y-axis are marked from -5 to 5. - **Slope:** - A slope of \(\frac{1}{3}\) indicates that for each unit increase in \(x\), \(y\) increases by \(\frac{1}{3}\). - **Y-Intercept:** - The line crosses the y-axis at \(y = -2\). **Plotting Points for the Line:** 1. **Start at the y-intercept (0, -2):** - This is the point where the line crosses the y-axis. 2. **Use the slope to find a second point:** - From (0, -2), move right by 3 units and up by 1 unit to reach the point (3, -1). 3. **Draw the line:** - Connect these points with a straight line, extending it in both directions through the grid. This graph provides a visual representation of the linear relationship defined by the equation \(3y - 1x = -6\), showing a positive slope and alignment with the calculated y-intercept.
Transcribed Image Text:**Graphing the Line \(3y - 1x = -6\)** This image demonstrates how to graph the linear equation \(3y - 1x = -6\) on a coordinate plane. **Equation Breakdown:** 1. **Rearrange the equation:** - Start by solving for \(y\): - \(3y = x - 6\) - \(y = \frac{1}{3}x - 2\) 2. **Identify the slope and y-intercept:** - The equation \(y = \frac{1}{3}x - 2\) is in slope-intercept form \(y = mx + b\). - Slope \(m = \frac{1}{3}\) - Y-intercept \(b = -2\) **Graph Details:** - **Axes:** - The x-axis and y-axis are marked from -5 to 5. - **Slope:** - A slope of \(\frac{1}{3}\) indicates that for each unit increase in \(x\), \(y\) increases by \(\frac{1}{3}\). - **Y-Intercept:** - The line crosses the y-axis at \(y = -2\). **Plotting Points for the Line:** 1. **Start at the y-intercept (0, -2):** - This is the point where the line crosses the y-axis. 2. **Use the slope to find a second point:** - From (0, -2), move right by 3 units and up by 1 unit to reach the point (3, -1). 3. **Draw the line:** - Connect these points with a straight line, extending it in both directions through the grid. This graph provides a visual representation of the linear relationship defined by the equation \(3y - 1x = -6\), showing a positive slope and alignment with the calculated y-intercept.
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