Question

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: Calculate the slope for part A

For the points \((3,12)\) and \((4,16)\), let \(x_1 = 3,y_1=12,x_2 = 4,y_2 = 16\).

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Step3: Calculate the slope for part B (first pair of points)

For the points \((1,4)\) and \((3,12)\), let \(x_1 = 1,y_1 = 4,x_2=3,y_2 = 12\).

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Step4: Compare the slopes

The slope between \((3,12)\) and \((4,16)\) is \(m = 4\) (from part A), and the slope between \((1,4)\) and \((3,12)\) is \(m_1=4\).

Answer:

• Part A: The slope is \(4\).
• Part B: Yes, the slope between \((1,4)\) and \((3,12)\) is the same as the slope between \((3,12)\) and \((4,16)\). The slope between \((1,4)\) and \((3,12)\) is \(\frac{12 - 4}{3 - 1}=\frac{8}{2} = 4\), and the slope between \((3,12)\) and \((4,16)\) is \(\frac{16 - 12}{4 - 3}=\frac{4}{1}=4\). So they are equal.