Question

a bucket is being filled with water. the graph below shows the water height (in mm) versus the time the water has been running (in seconds). use the graph to answer the questions. (a) how much does the height of the water increase for each second the water is running? mm (b) what is the slope of the line?

Explanation:

Step1: Analyze the graph's slope

The graph is a straight line through the origin, so we can use two points. Let's take (1, 4) and (2, 8) (estimating from the grid). The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate the slope for part (a) and (b)

For part (a), the increase per second is the slope. Using (0,0) and (4, 16) (since at 4 seconds, height is 16 mm), $m = \frac{16 - 0}{4 - 0} = 4$. So each second, height increases by 4 mm. For part (b), the slope is also 4, as it's the rate of change.

Answer:

(a) 4
(b) 4