Compare the graphs of the inverse variations. Please provide at least 3 comparisons
y= (-0.2/x) and y= (-0.3/x)
-0.05, -0.075 , -0.1, -0.15 ?
To compare the graphs of inverse variations, we need to analyze the equations and understand how they are related.
First, let's compare the given equations:
1. Equation 1: y = (-0.2/x)
2. Equation 2: y = (-0.3/x)
Now, let's identify three comparisons between these two equations:
1. Coefficient: The coefficient in Equation 2, -0.3, is greater in magnitude than the coefficient in Equation 1, -0.2. This means that Equation 2 will yield larger values of y compared to Equation 1 for the same x-values. Consequently, the graph of Equation 2 will have a steeper slope than the graph of Equation 1.
2. y-intercept: In both equations, when x approaches infinity or negative infinity, y approaches zero. This means that both graphs will intersect the y-axis at zero. Therefore, both equations share the same y-intercept.
3. Asymptotes: In both equations, the denominator (x) approaches zero as x approaches infinity or negative infinity. As a result, both equations have a vertical asymptote at x = 0. This means that the graphs of the equations will approach the y-axis closely but never touch it.
To summarize, the three comparisons between the graphs of the given inverse variation equations are:
1. Equation 2 has a steeper slope than Equation 1.
2. Both equations share the same y-intercept (y = 0).
3. Both equations have a vertical asymptote at x = 0.