Question

1 the table shows the number of pages adriano read in x hours. graph the data. then find the slope of the line. explain what the slope represents. (example 1)
time (h) | 1 | 2 | 3 | 4
number of pages | 50 | 100 | 150 | 200

1. graph the data. find the numerical value of the slope and interpret it in words. (example 2)

number of yards | 1 | 2 | 3
number of feet | 3 | 6 | 9

3 the graph shows the average speed of two cars on the highway.
a. what does (2, 120) represent?
b. what does (1.5, 67.5) represent?
c. what does the ratio of the y - coordinate to the x - coordinate for each pair of points on the graph represent?
d. what does the slope of each line represent?
e. which car is traveling faster? how can you tell from the graph?

Explanation:

Problem 1

Step1: Identify coordinate pairs

Pairs: $(1,50), (2,100), (3,150), (4,200)$

Step2: Calculate slope formula

Slope $m = \frac{y_2-y_1}{x_2-x_1}$

Step3: Substitute two points

$m = \frac{100-50}{2-1} = \frac{50}{1} = 50$

Step4: Interpret the slope

Slope = pages per hour read

Step1: List coordinate pairs

Pairs: $(1,3), (2,6), (3,9)$

Step2: Apply slope formula

Slope $m = \frac{y_2-y_1}{x_2-x_1}$

Step3: Plug in point values

$m = \frac{6-3}{2-1} = \frac{3}{1} = 3$

Step4: Interpret the slope

Slope = feet per yard

a. The graph has $x$ as time (hours) and $y$ as distance (miles), so the coordinate corresponds to time and distance for one car.
b. Using the same axis definitions, this coordinate maps time to distance for the other car.
c. The ratio $\frac{\text{distance}}{\text{time}}$ is the standard formula for average speed.
d. Slope of a distance-time graph is calculated as $\frac{\text{change in distance}}{\text{change in time}}$, which equals average speed.
e. A steeper line on a distance-time graph means a greater rate of distance covered over time, i.e., higher speed.

Answer:

The slope is 50, which represents Adriano reading 50 pages per hour.

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Problem 2