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

Rearranging the Equation:
2x + 6y = 8
6y = -2x + 8
y = (-2/6)x + 8/6
y = (-1/3)x + 4/3

Plotting the Graph:
Now that we have the equation in the form y = mx + c, we can plot the graph. The y-intercept is 4/3, which means the line crosses the y-axis at the point (0, 4/3). The slope is -1/3, which means for every unit increase in x, y decreases by 1/3.

Key Points to Plot the Graph:
- Start by plotting the y-intercept at (0, 4/3)
- Use the slope to find another point on the line, for example, if x=3, y would be 3/3 = 1
- Connect the two points to draw the line representing the equation 2x + 6y = 8

Interpreting the Graph:
The graph of 2x + 6y = 8 is a straight line passing through the points (0, 4/3) and (3, 1). It shows all possible solutions to the equation, where every point on the line satisfies the equation. This graphical representation helps in visualizing the relationship between x and y values in the given equation.