How to Graph the Linear Equation x + 3y = 6

How to Graph the Linear Equation x + 3y = 6 To graph the linear equation x + 3y = 6, follow these steps: 1. *Rewrite the equation in slope-intercept form (y = mx + b):* Start with the given equation: x + 3y = 6 Solve for y by isolating it on one side: 3y = -x + 6 y = (-1/3)x + 2 Now the equation is in slope-intercept form: y = (-1/3)x + 2. 2. *Identify the slope and y-intercept:* From the equation y = (-1/3)x + 2: The slope (m) is -1/3. The y-intercept (b) is 2. 3. *Plot the y-intercept:* The y-intercept is the point where the line crosses the y-axis. So, plot the point (0, 2) on the graph. 4. *Use the slope to find another point:* The slope is -1/3, which means that for every 3 units you move horizontally to the right (along the x-axis), the line moves 1 unit down (along the y-axis). From the point (0, 2), move 3 units to the right along the x-axis and 1 unit down along the y-axis to get the point (3, 1). 5. *Plot the second point:* Plot the point (3, 1) on the graph. 6. *Draw the line:* Draw a straight line through the points (0, 2) and (3, 1). Extend the line in both directions to complete the graph. 7. *Optional – Plot more points:* You can plot additional points using the slope to ensure the line is correct. For example, move another 3 units to the right and 1 unit down, or move in the opposite direction. Now, you have the graph of the equation x + 3y = 6.