The double intercept approach is a graphical method used to plot linear equations by finding the points where the graph intersects the axes (the x-intercept and y-intercept).
In the case of the equation y = 1/x, it is important to clarify that this is not a linear equation but rather a hyperbola. However, we can still use similar concepts to understand its graph.
To illustrate the relationship between x and y in this equation, we can determine a few key points:
- When x = 1, then y = 1/1 = 1. So, we have the point (1, 1).
- When x = -1, then y = 1/(-1) = -1. This gives us the point (-1, -1).
- When x = 2, then y = 1/2 = 0.5. This corresponds to the point (2, 0.5).
- When x = -2, then y = 1/(-2) = -0.5. This gives us the point (-2, -0.5).
Now, if we attempt to plot these points, we will notice a pattern. As x increases, y gets smaller (approaching 0 but never reaching it), and as x decreases (in the negative range), y behaves similarly. These properties suggest that the graph consists of two distinct curves: one in the first quadrant and another in the third quadrant.
The graph will asymptotically approach both the x-axis and y-axis, meaning it will get very close to them but will never touch or cross these axes. This characteristic defines the hyperbola formed by the equation.
In summary, using the double intercept approach allows us to identify key points on the graph of y = 1/x, even though it transforms into a hyperbolic shape rather than a straight line graph. These points can then be plotted to visualize the relationship between x and y more clearly.