Compare the graphs of the inverse variations by comparing asymptotes, similar points, lines of reflections, and quadrants.
y=-0.7/x and y=-0.9/x
To compare the graphs of the inverse variations given by y = -0.7/x and y = -0.9/x, you can analyze their asymptotes, similar points, lines of reflections, and quadrants.
1. Asymptotes:
The graph of y = -0.7/x has two asymptotes: the x-axis (y = 0) and the y-axis (x = 0). This means that the graph approaches but never intersects these lines as x and y values become larger or smaller.
Similarly, the graph of y = -0.9/x also has x and y-axis as asymptotes.
2. Similar Points:
When comparing similar points between the two graphs, you can choose specific x-values and find the corresponding y-values for each equation.
For example, let's consider x = 1. When x = 1, y = -0.7/1 = -0.7 for the first equation, and y = -0.9/1 = -0.9 for the second equation. So, the similar point for x = 1 is (1, -0.7) for the first equation and (1, -0.9) for the second equation.
3. Lines of Reflections:
The lines of reflection occur when you interchange the x and y coordinates. For example, if (a, b) is a point on the graph of y = -0.7/x, then (b, a) will be a point on the graph after reflecting it across the line y = x.
Similarly, the same reflection holds for the equation y = -0.9/x.
4. Quadrants:
To determine the quadrants, you need to analyze the signs of x and y values, either by choosing specific values or looking at the equation. In both cases, the x and y values are negative, resulting in the graph lying in the third and second quadrants.
Overall, the graphs of y = -0.7/x and y = -0.9/x exhibit similar asymptotes, similar points at specific x-values, lines of reflection when interchanging x and y coordinates, and lie in the third and second quadrants.