Final answer:
The relationship between the given x and y values is described by the linear equation y = 2x + 2. This equation accurately represents the pattern where every increment of 2 in x corresponds to an increase of 2 in y, with an additional 2 added, representing the y-intercept.
Step-by-step explanation:
To determine the correct equation that represents the relationship between x and y for the points given in the graph (X=1,3,5,7 and Y=4,6,8,10), we can observe the pattern of the change in y as x increases. Since for every increment by 2 in x, y increases by 2, this suggests a linear relationship with a slope (m) of 1. However, when x is 1, y is not 1 but 4, meaning there is an additional constant value, known as the y-intercept (b).
Multiplying x by 2 would give us values of y that are twice as large as the corresponding x, which are 2, 6, 10, and 14, respectively, and not the values we have (4, 6, 8, 10). Therefore, we need to adjust the equation by adding or subtracting a constant to match our y values. By inspection, we can see that each y value is 2 units larger than twice the x value.
Therefore, the correct equation is y = 2x + 2. This matches the given pattern entirely, verifying that for x=1, y=4 (2*1 + 2 = 4); for x=3, y=6 (2*3 + 2 = 8), and so on. This is Option 1 from the provided choices.