Final answer:
The y coordinate's relationship with the x coordinate is analyzed in three sets: (a) has a linear relationship y=7x, (b) does not have an obvious relationship, and (c) shows that y varies independently from a constant x value (9). By plotting points such as (1,5), (2,10), (3,7), and (4,14), one can visualize the dependence of y on x.
Step-by-step explanation:
The relationship between the y coordinate and the x coordinate in a list of coordinates can be understood by observing patterns or applying a mathematical rule. Let's analyze the given lists:
- For set (a) with points like (1,7) (2,14) (3,21) (0,0) (-4,-28), we notice that the y coordinate is always seven times the x coordinate. It suggests the dependence of y on x is linear, represented by the equation y = 7x.
- In set (b) with points (3,7) (2,8) (10,0) (-1,11) (6,4), there is no obvious single rule that links x and y, indicating that the relationship is not linear and the dependence of y on x may not be represented by a simple equation.
- For set (c) with points (9,1) (9,0) (9,-5) (9,6) (9,1/2), the x coordinate is constant at 9, and the y coordinate varies independently. This suggests a vertical line on a graph, where y is independent of x.
To understand these relationships visually, points can be plotted on a graph and connected, showing how y changes in relation to x. The graphical representation can indicate whether the relationship is linear, nonlinear, or independent. For example, if we plot points (1,5), (2,10), (3,7), and (4,14), we can observe how y varies with x and determine the nature of their relationship.