Which function has the greatest rate of change?
Responses
A y = 3x - 4y = 3x - 4
B 4y - 8x = 14y - 8x = 1
C a line passing through points (2,6) and (3,10)a line passing through points (2,6) and (3,10)
D a line passing through points (5,−2) and (6, 4)
To determine which function has the greatest rate of change, we need to compare the slopes of the lines represented by each function.
A: The equation y = 3x - 4 has a slope of 3. So, the rate of change is 3.
B: The equation 4y - 8x = 1 can be rewritten as y = 2x + 1/4, which has a slope of 2. So, the rate of change is 2.
C: The line passing through points (2,6) and (3,10) has a slope of (10-6)/(3-2) = 4/1 = 4. So, the rate of change is 4.
D: The line passing through points (5,−2) and (6, 4) has a slope of (4-(-2))/(6-5) = 6/1 = 6. So, the rate of change is 6.
Therefore, the function with the greatest rate of change is D: a line passing through points (5,−2) and (6, 4).