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 2. 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 slope formula

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

Step2: Pick two data points

Use $(1,50)$ and $(2,100)$

Step3: Calculate slope

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

Step4: Interpret the slope

Slope = pages per hour read

Step1: Recall slope formula

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

Step2: Select two data points

Use $(1,3)$ and $(2,6)$

Step3: Compute the slope

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

Step4: Interpret the slope

Slope = feet per yard conversion

a. The x-axis is time (hours) and y-axis is distance (miles); the point aligns with Car A's line.
b. The x-axis is time (hours) and y-axis is distance (miles); the point aligns with Car B's line.
c. The ratio $\frac{\text{distance}}{\text{time}}$ is the standard formula for speed.
d. Slope of a distance-time graph equals $\frac{\text{change in distance}}{\text{change in time}}$, which is speed.
e. A steeper line on a distance-time graph means greater speed per unit time.

Answer:

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

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Problem 2