The graph of the direct variation equation y = 52x is a straight line that passes through the origin (0, 0). This type of equation represents a direct relationship between the variables x and y, where the constant of variation is 52.
In this case, for every unit increase in x, y increases by 52 units. The slope of the line is 52, which means that for each step you take to the right along the x-axis, the line rises significantly. This gives the graph a steep incline.
To plot this graph, you can start by choosing a few values for x, calculating the corresponding y values, and then plotting those points:
- If x = 1, then y = 52(1) = 52.
- If x = -1, then y = 52(-1) = -52.
- If x = 0, then y = 52(0) = 0.
Connecting these points with a straight line will give you the graph of the equation. The line will extend infinitely in both directions, representing all possible values of x and y that satisfy the equation. Since this is a direct variation, the graph will always go through the origin, reinforcing the idea that when x is zero, y is also zero.