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) what is the slope of the line? (b) how much does the height of the water increase for each second the water is running? mm

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the origin \((0, 0)\) and another point, say \((7, 35)\) (assuming the end point is at \(x = 7\) seconds and \(y = 35\) mm).

Step2: Calculate the slope

The formula for slope \(m\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, 0)\) and \((7, 35)\), we have \(x_1 = 0\), \(y_1 = 0\), \(x_2 = 7\), \(y_2 = 35\). So \(m=\frac{35 - 0}{7 - 0}=\frac{35}{7}=5\).

Step3: Interpret the slope for part (b)

The slope of a line in a graph of height (y - axis) vs. time (x - axis) represents the rate of change of height with respect to time. So the height increase per second is equal to the slope.

Answer:

s:
(a) The slope of the line is \(\boldsymbol{5}\).

(b) The height of the water increases by \(\boldsymbol{5}\) mm for each second the water is running.