To determine whether the relationship between x=6 and y=20 is a linear function, we need to check if the ratio of the change in y to the change in x is constant.
Let's calculate the ratio of the change in y to the change in x using two more points on the same line.
Suppose we have another point on the line with coordinates (x1, y1) = (2, 8). Then the ratio of the change in y to the change in x is:
(y - y1) / (x - x1) = (20 - 8) / (6 - 2) = 12 / 4 = 3
Now, suppose we have another point on the line with coordinates (x2, y2) = (10, 32). Then the ratio of the change in y to the change in x is:
(y2 - y) / (x2 - x) = (32 - 20) / (10 - 6) = 12 / 4 = 3
Since the ratio of the change in y to the change in x is constant and equal to 3 for any two points on the line, we can conclude that the relationship between x=6 and y=20 is a linear function.
We can find the equation of the line passing through the two points (2, 8) and (6, 20) using the slope-intercept form:
slope = (y2 - y1) / (x2 - x1) = (20 - 8) / (6 - 2) = 3
y - y1 = slope * (x - x1)
y - 8 = 3(x - 2)
y = 3x + 2
Therefore, the relationship between x=6 and y=20 is described by the linear function y = 3x + 2.