a line that passes through (3,3) and (4,0)

Question

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

Answer 1

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.