The equation y = 52x represents a direct variation, which means that the value of y varies directly with the value of x. In simpler terms, if you increase x, y increases proportionally to that change, and vice versa.
To visualize this, the graph of the equation will be a straight line that passes through the origin (0,0). The slope of this line, which represents the factor by which y changes for a given change in x, is equal to 52. This means that for every 1 unit increase in x, y increases by 52 units.
In terms of appearance, the line will be quite steep because of the large slope value of 52. If you were to plot a few points for x values:
- If x = 1, then y = 52 imes 1 = 52.
- If x = 2, then y = 52 imes 2 = 104.
- If x = -1, then y = 52 imes -1 = -52.
Plotting these points: (1, 52), (2, 104), and (-1, -52) will help illustrate how the line behaves. As x increases, y skyrockets, and as x decreases, y drops significantly, creating that steep slope.
In summary, the graph of y = 52x is a straight line through the origin with a steep slope of 52, illustrating the principle of direct variation where y is directly proportional to x.