a line that passes through (3,3) and (4,0)
X Y
-4 0
-3 -0.25
-2 -0.5
-1 -0.75
0 -1
A: both functions are decreasing and have different rates of change
B: both functions are increasing and have different rates of change
C: both functions are increasing and have the same rates of change
D: both functions are decreasing and the same rate of change
To determine the answer, let's find the equation of the line that passes through the points (3,3) and (4,0).
Using the formula for the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, let's input the point (3,3) and (4,0) into the formula:
For the point (3,3):
y - 3 = m(x - 3)
For the point (4,0):
0 - 3 = m(4 - 3)
Simplifying the equation:
-3 = m
So, the equation of the line is y - 3 = -3(x - 3). Simplifying this equation further, we get y - 3 = -3x + 9.
Now, let's check the options provided:
A: both functions are decreasing and have different rates of change - This is not correct, as the function is not decreasing and the rates of change are not different.
B: both functions are increasing and have different rates of change - This is not correct, as the function is not increasing.
C: both functions are increasing and have the same rates of change - This is not correct, as the function is not increasing.
D: both functions are decreasing and the same rate of change - This is the correct answer, as the function is decreasing and has a slope of -3, which means it has the same rate of change.