y=3
a line which passes through (3,6) and (4,7)
A: the rates of change are the same, but the Y intercepts are different
B: the items have the same Y intercepts, and the same rate of change
C: the items have different Y intercepts, a different rates of change
D: the Y intercepts are the same, but the rates of change are different
The correct answer is D: the Y intercepts are the same, but the rates of change are different.
To find the rate of change (slope) between two points on a line, we can use the formula:
slope = (change in y)/(change in x)
In this case, we can calculate the slope between the two given points:
slope = (7-6)/(4-3) = 1/1 = 1
Therefore, the rate of change between the two points is 1.
However, since the y-coordinate is 3, the y-intercept is also 3. Therefore, the y-intercepts are the same.
Therefore, the correct answer is D: the Y intercepts are the same, but the rates of change are different.