Which pairs of points would result in a line with a rate of change of 2:1? Select all that apply.
A. (−4,−11) and (−2,−7)
B. (5, 6) and (−5, 12)
C. (0, −3) and (−4,−11)
D. (0,−3) and (5,7)
just apply the slope formula for each pair, and check...
To determine the rate of change between two points, we calculate the difference in the y-values and divide it by the difference in the x-values.
Let's calculate the rates of change for each pair of points:
A. (−4,−11) and (−2,−7):
Rate of change = (−7 − (−11)) / (−2 − (−4)) = 4 / 2 = 2
B. (5, 6) and (−5, 12):
Rate of change = (12 − 6) / (−5 − 5) = 6 / −10 = −3/5
C. (0, −3) and (−4,−11):
Rate of change = (−11 − (−3)) / (−4 − 0) = −8 / −4 = 2
D. (0,−3) and (5,7):
Rate of change = (7 − (−3)) / (5 - 0) = 10 / 5 = 2
From the above calculations, we find that pairs A, C, and D both have a rate of change of 2:1. So the correct answers are:
A. (−4,−11) and (−2,−7)
C. (0, −3) and (−4,−11)
D. (0,−3) and (5,7)