Final answer:
To find how many units to the right from the point (0,6) one needs to move to stay on a line with slope a, divide the vertical change (6 units) by the slope (a), resulting in a horizontal movement of 6/a units to the right.
Step-by-step explanation:
The student is asking about the concept of slope in a Cartesian coordinate system, which is a fundamental concept in algebra and coordinate geometry. Since the given line t has a slope of a and passes through the origin (0,0), we can determine the position relative to this line after moving up 6 units from the origin.
The formula to calculate the slope (m) of a line is:
m = (change in y)/(change in x)
Considering the line passes through (0,0), if we move up 6 units, we are at point (0,6). To find the horizontal distance to the right we would move to stay on the line with slope a, we rearrange the slope formula to solve for the change in x:
change in x = (change in y) / m
Since we have moved up 6 units (change in y = 6), and the slope of the line is a:
change in x = 6 / a
Therefore, to stay on line t, we would need to move to the right by 6/a units from point (0,6).