Answer:
C. Same y-intercept; same rate of change
Explanation:
You want to compare y-intercepts and rates of change for the equation y=1/2x and a table with (x, y) values (0, 0) and (2, 1).
Y-intercepts
The equation has a y-intercept of 0. When x=0, y = 1/2(0) = 0.
The table shows the y-intercept to be 0. When x=0, y = 0.
Rates of change
The equation has a slope (x-coefficient) of 1/2.
The table has a rate of change of y/x = 1/2.
The y-intercepts and rates of change are the same.
__
Additional comment
The rate of change for the table is y/x only because the y-intercept is zero. If it were not zero, then the rate of change would be found from ...
slope = (y2 -y1)/(x2 -x1)
For the first two lines of the table, this is ...
slope = (1 -0)/(2 -0) = 1/2