To analyze the data provided, we can look for patterns and create a linear equation based on those observations.
Given Data:
- Time (x): 4, 3, 10, 7, 9 (minutes)
- Distance (y): 76, 57, 190, 133, 171 (meters)
a. Every minute, ___ meters are traveled.
To find the average distance traveled per minute, we can calculate the slope (rate of change).
- Calculate a few slopes between the data points:
- From (4, 76) to (3, 57): \[ \text{slope} = \frac{57 - 76}{3 - 4} = \frac{-19}{-1} = 19 \text{ meters per minute} \]
- From (3, 57) to (10, 190): \[ \text{slope} = \frac{190 - 57}{10 - 3} = \frac{133}{7} \approx 19 \text{ meters per minute} \]
- It appears the distance traveled per minute is consistently around 19 meters, so we can conclude:
Every minute, 19 meters are traveled.
b. Write an equation to show the relationship between x and y.
We can use the slope-intercept form of a linear equation y = mx + b, where m is the slope and b is the y-intercept.
Using the slope we calculated (approximately 19 meters per minute), we can also choose one point to find the y-intercept. Let's use the point (4, 76):
\[ 76 = 19(4) + b \Rightarrow 76 = 76 + b \Rightarrow b = 0 \]
So, the equation is: \[ y = 19x + 0 \quad \text{or simply} \quad y = 19x \]
c. This relationship is ______ because the y-intercept is ______.
The relationship is linear because it can be expressed in the form of a linear equation, and the y-intercept is 0 (since the equation simplifies to y = 19x).
Summary of the Responses
a. Every minute 19 meters are traveled.
b. Write an equation to show the relationship between x and y: y = 19x
c. This relationship is linear because the y-intercept is 0.
1 answer