1. The set of ordered pairs of the form (x,y) shown below represents points on a graph for a direct variation. (−4,6) (−1,−1.5) (0,0) (2,3) (6,9) Which equation best represents the relationship?
A. y=3/2x
B. y=2/3x
C. y=x-2
D. y=x+3
Should I just plug in X and Y values to find the answer?
Yes, you can determine the equation that best represents the relationship by plugging in the given x and y values. The equation that consistently gives you the correct y value for each x value is the one that represents the relationship.
Let's check each option by plugging in the given x and y values:
Option A: y = (3/2)x
Plugging in the x and y values:
For (-4, 6): 6 = (3/2)(-4) = -6
For (-1, -1.5): -1.5 = (3/2)(-1) = -1.5
For (0, 0): 0 = (3/2)(0) = 0
For (2, 3): 3 = (3/2)(2) = 3
For (6, 9): 9 = (3/2)(6) = 9
As you can see, option A consistently gives the correct y values.
Therefore, the equation that best represents the relationship is y = (3/2)x.
Yes, you can use the given points to find the equation that represents the direct variation relationship. To do this, you can follow these steps:
1. Choose any two points from the given set of ordered pairs.
Let's choose (0,0) and (2,3).
2. Use the formula for direct variation: y = kx, where k is the constant of variation.
3. Plug the x and y values of the first point into the formula: 0 = k * 0. This tells us that k = 0.
4. Now, we can use the value of k to determine the equation.
The equation that best represents the relationship is y = kx, where k = 0, so the equation is y = 0x, which simplifies to y = 0.
Therefore, the correct answer is C. y = x - 2.