4. Given the table for x, time in minutes, and y, distance traveled:

Question

x: time 8 5 7 2 9
y: distance 664 415 581 166 747


(4 points)
a. Every minute
meters are traveled.

b. Write an equation to show the relationship between x and y:
.

c. This relationship is
because the y-intercept is

Answer 1

To analyze the data and answer the questions, we can follow these steps:

Given Data

• Time (x) in minutes: 8, 5, 7, 2, 9
• Distance (y) in meters: 664, 415, 581, 166, 747

a. Every minute, ___ meters are traveled.

To determine the average speed of travel in meters per minute, we can calculate the average distance traveled per minute based on the provided data.

1. Calculate Total Distance and Total Time:

   • Total distance $=664+415+581+166+747=2573,\text{meters}$
   • Total time $=8+5+7+2+9=31,\text{minutes}$

2. Average Speed (meters per minute): $$\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}=\frac{2573,\text{meters}}{31,\text{minutes}}\approx 83.3,\text{meters/minute}$$

Answer: Every minute approximately 83.3 meters are traveled.

b. Write an equation to show the relationship between x and y:

To find a linear equation that models the relationship between distance (y) and time (x), we can use the form of the linear equation:

$$y=mx+b$$

Where:

• $m$ is the slope (average speed)
• $b$ is the y-intercept (distance at time 0)

Using the average speed we just calculated:

• $m\approx 83.3$

To calculate $b$, we can inspect the data and see if we can derive the y-intercept. If we were to extrapolate back to $x=0$ using the average speed, we can treat $b$ as 0 for simplification in the absence of more specific rules-data.

However, to derive the exact relationship and y-intercept, we commonly perform linear regression or calculate based on existing data points. Given the nature, if we take, for simplicity, $b=0$:

Thus, an approximate equation might be: $$y=83.3x+0$$

Answer: The equation is $y=83.3x$ (for a simple approximation). More analysis may adjust the slope and the intercept based on real data fitting.

c. This relationship is ____ because the y-intercept is ____.

• The relationship is linear (assuming a straight-line correlation).
• The y-intercept is 0 (if we assume distance starts at 0 when time is 0 in a simplest context; else calculation of $b$ may provide a more accurate non-zero intercept).

Answer: This relationship is linear because the y-intercept is 0 (or as derived from regression fitting, needs calculation).

For more accurate results, graphical analysis or statistical regression would provide precise figures.