Question

a proportional relationship has a constant rate. that means the distance increases by the same amount for each minute of rowing.
describe cole’s rate. how far does he row per minute?
cole rows? meters per minute.
(chart: x - time (min), y - distance (m); line from (0,0) with points like (1,200) etc.)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that when time \( t = 1 \) minute, distance \( d = 200 \) meters. Another point is the origin \((0,0)\).

Step2: Calculate the rate (slope)

The rate (speed) is the slope of the distance - time graph, which is given by the formula \( \text{rate}=\frac{\text{change in distance}}{\text{change in time}} \). Using the points \((0,0)\) and \((1,200)\), we have \( \text{rate}=\frac{200 - 0}{1 - 0}=\frac{200}{1} = 200 \) meters per minute. We can also check with other points. For example, when \( t = 2 \) minutes, \( d = 400 \) meters. Then \( \text{rate}=\frac{400 - 0}{2 - 0}=\frac{400}{2}=200 \) meters per minute. When \( t = 3 \) minutes, \( d = 600 \) meters, \( \text{rate}=\frac{600 - 0}{3 - 0}=\frac{600}{3} = 200 \) meters per minute. When \( t=4 \) minutes, \( d = 800 \) meters, \( \text{rate}=\frac{800 - 0}{4 - 0}=\frac{800}{4}=200 \) meters per minute.

Answer:

Cole rows at a constant rate of 200 meters per minute.