Question

1. a machinist measures the thickness of a grinding pad every week. the graph shows how many millimeters the grinding pad has worn down.

a. what is the slope of the line?
b. apply math models what does the slope mean?

1. higher order thinking you use a garden hose to fill a circular wading pool that is 83.6 cm deep. you measure the depth of the water in the pool every 2 minutes. the table shows the data.

a. what is the slope of the line that represents the change in the depth of the water?
b. what does this slope mean?
c. how many minutes will it take to fill the pool?

1. the graph shows the number of kilometers gina swims. what is the slope of the line and what does it mean?

assessment practice

1. donald graphs the distance he walks over time. the graph passes through the points (3, 12) and (4, 16).

part a
find the slope of the line that passes through these points.
part b
is the slope between (1, 4) and (3, 12) the same as the slope between (3, 12) and (4, 16)? explain.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.

Step2: Substitute the points \((3,12)\) and \((4,16)\) into the formula

Let \((x_1 = 3,y_1 = 12)\) and \((x_2=4,y_2 = 16)\). Then \(m=\frac{16 - 12}{4 - 3}\).

Step3: Calculate the slope

\(m=\frac{4}{1}=4\).

Step4: For the points \((1,4)\) and \((3,12)\)

Let \((x_1 = 1,y_1 = 4)\) and \((x_2 = 3,y_2=12)\). Then \(m=\frac{12 - 4}{3 - 1}=\frac{8}{2}=4\).

Answer:

Part A: The slope of the line passing through \((3,12)\) and \((4,16)\) is \(4\).
Part B: The slope between \((1,4)\) and \((3,12)\) is \(\frac{12 - 4}{3 - 1}=4\), and the slope between \((3,12)\) and \((4,16)\) is \(\frac{16 - 12}{4 - 3}=4\). So, the slopes are the same.