Graphical Representation of the Linear Equation 2x + 6y = 8
To represent the linear equation 2x + 6y = 8 graphically, we need to first convert it into the slope-intercept form, y = mx + c, where m is the slope and c is the y-intercept.

Converting the Equation to Slope-Intercept Form
2x + 6y = 8
6y = -2x + 8
y = -1/3x + 4/3

Plotting the Graph
Now that we have the equation in slope-intercept form, we can plot the graph by following these steps:
1. Start by plotting the y-intercept at y = 4/3 on the y-axis.
2. Determine a second point on the line by moving the slope -1/3 units down and 1 unit to the right from the y-intercept.
3. Connect the two points with a straight line to represent the graph of the equation 2x + 6y = 8.

Interpreting the Graph
The graph of the equation 2x + 6y = 8 will be a straight line with a negative slope of -1/3. It shows all the possible solutions (x, y) that satisfy the equation. Any point on the line is a solution to the equation, and any point off the line is not a solution.
In conclusion, by plotting the graph of the linear equation 2x + 6y = 8, we can visually represent the relationship between x and y values that satisfy the equation.