Question

Which line has the greatest rate of change? A line passing through (-1, 4) and (1, 7). A line passing through (1, 3) and (5, 11). A line passing through (1, 1) and (4, -3). A line passing through (0, 6) and (12, 9). please help!!

Answer 1

A line passing through (1, 3) and (5, 11)

Rate of change = 2

Explanation:

• Rate of change = change in y / change in x
• r = Δy/Δx

Let's get the rate of change for each line:

A line passing through (-1, 4) and (1, 7).

• r = (7 - 4) / (1 -(-1)) = 3/2

A line passing through (1, 3) and (5, 11).

• r = (11 - 3) / (5 - 1) = 8/4 = 2

A line passing through (1, 1) and (4, -3).

• r = (- 3 - 1) / (4 - 1) = -4/3

A line passing through (0, 6) and (12, 9)

• r = (9 - 6) / (12 - 0) = 3/12 = 1/4

Comparing the values of r, we can see the greatest one is 2 for the line passing through (1, 3) and (5, 11)