In this set of eight problems, we have to match each equation with the correct description of its graph. However, these are test corrections I'm doing and I do not have the previous multiple choice answers so I can deduct from it, but can someone help me?
The equation is xy = 8.
The descriptions that I KNOW are possible are:
A. Parabola with axis x = 0
B. Circle with center (2,-1)
C. Hyperbola with axes as asymptotes
F. Line with slope 3/2
G. Parabola with vertex (2,-1)
H. Circle with center (0,0), radius 4
Okay, I'm pretty sure B and H can be ruled out because the equation doesn't look like that of an equation for a circle. However, I'm not so sure for the others. Any help is GREATLY appreciated!!!!!!!!!!!!!! :D
make a table of values to find a suitable number of ordered pairs to plot, and you will see that C is the correct answer.
Ohhh ok I think I get it now thanks Reiny!! :D
To determine the correct description of the graph of the equation xy = 8, you can analyze the equation and compare it with the given descriptions.
Let's begin by examining the equation xy = 8.
This equation is in the form of a product, where x and y are multiplied to equal 8. This means that for any value of x, when multiplied by its corresponding value of y, the result will always be 8.
To further analyze the equation, let's consider different values for x and y.
If x = 1, then y must equal 8, since 1 multiplied by 8 is 8. Thus, one point on the graph would be (1, 8).
If x = -1, then y must equal -8, since -1 multiplied by -8 is also 8. Therefore, another point on the graph would be (-1, -8).
By finding more points in a similar manner, you will notice that the graph of xy = 8 is a rectangular hyperbola. In this case, the hyperbola has its asymptotes aligned with the coordinate axes because the equation does not have any additional terms that would shift it.
Therefore, based on the given descriptions, the correct match for the equation xy = 8 would be C: Hyperbola with axes as asymptotes.