Given the table for x, time in minutes, and y, distance traveled: 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 .
a. To find the distance traveled per minute, we can divide the distance (y) by the time (x) for each pair of values.
ratio = y/x
For the given values:
ratio1 = 664/8 = 83 meters/minute
ratio2 = 415/5 = 83 meters/minute
ratio3 = 581/7 = 83 meters/minute
ratio4 = 166/2 = 83 meters/minute
ratio5 = 747/9 = 83 meters/minute
Therefore, 83 meters are traveled every minute.
b. To write an equation to show the relationship between x and y, we can use the formula:
y = mx + b
Where m is the slope (distance traveled per minute) and b is the y-intercept.
From part a, we found that the slope (m) is 83.
Using one of the points from the table, such as (8, 664), we can substitute the values into the equation:
664 = 83(8) + b
Simplifying the equation:
664 = 664 + b
b = 0
Therefore, the equation that represents the relationship between x and y is:
y = 83x + 0
c. Since the y-intercept (b) is 0, it means that the distance traveled (y) is 0 when the time (x) is 0. In other words, when no time has passed, no distance has been traveled.
c. This relationship is because the y-intercept is (0, 0) .
Yes, you are correct. The relationship between x and y is because the y-intercept is (0, 0). This means that when x (time) is 0, y (distance) is also 0.
the options is non proportional or proportional
Based on the given data, the relationship between x (time) and y (distance) is proportional. This is because the ratio of distance to time remains constant for all pairs of values. As calculated in part a, we found that the ratio of distance to time is consistently 83 meters/minute. Therefore, the relationship between x and y is proportional.
A cab company charges $12 per mile for a lift to the airport. What change would the company make to their charges to make this a non proportional situation? (1 point) Responses Charge $15 per mile instead of $12 Charge $15 per mile instead of $12 No changes are needed. No changes are needed. Charge $4 per mile instead of $12 Charge $4 per mile instead of $12 Charge a flat rate of $20 and then $12 per mile
To make this a non-proportional situation, the cab company would need to charge a flat rate in addition to the per mile charge.
Among the options given, the correct response would be: "Charge a flat rate of $20 and then $12 per mile."
This is because a flat rate of $20 is added to the per mile charge of $12, making the charges not directly proportional to the distance traveled.
One business charges $22 per t-shirt that is custom made. Another business charges $16 per t-shirt plus a $15 set up fee for custom made t-shirts. How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph? (1 point) Responses Down 15 Down 15 Right 4 Right 4 Up 4 Up 4 Down 4 Down 4 Up 15 Up 15 Left 15
To transform the first graph to make it non-proportional with the same y-intercept as the second graph, you would move it "Up 15 units".
The second business charges a $15 setup fee in addition to $16 per t-shirt. By moving the first graph up by 15 units, you would essentially add a $15 fee to the cost of each t-shirt, making it non-proportional.
To find the relationship between x and y, we can observe the table of values given. Let's start by looking at the pattern for x (time) and y (distance) columns:
x (time):
8, 5, 7, 2, 9
y (distance):
664, 415, 581, 166, 747
a. To find the number of meters traveled every minute, we can subtract the distance at the beginning of the given time period from the distance at the end of the time period, and divide it by the difference in time. Let's take the first and last data points:
Distance at the end of the time period = 747
Distance at the beginning of the time period = 664
Difference in time = 9 - 2 = 7 minutes
Now, let's calculate the distance traveled every minute:
Distance traveled every minute = (Distance at the end - Distance at the beginning) / Difference in time
Distance traveled every minute = (747 - 664) / 7
Distance traveled every minute = 83 / 7
Distance traveled every minute ≈ 11.86 meters
Therefore, every minute, approximately 11.86 meters are traveled.
b. To write an equation showing the relationship between x and y, we can use the concept of linear regression. We'll use the least squares method to find the equation of the line that best fits the given data points.
Let's list the (x, y) pairs from the given table:
(8, 664), (5, 415), (7, 581), (2, 166), (9, 747)
Using these points, we can find the equation of the line using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we'll find the difference in y divided by the difference in x between two points. Let's take the first and last data points:
m = (747 - 664) / (9 - 8)
m = 83 / 1
m = 83
Now, let's find the y-intercept using the formula y = mx + b. We'll use one of the given points (5, 415):
415 = (83)(5) + b
415 = 415 + b
b = 0
So the equation showing the relationship between x and y is:
y = 83x
c. Since the y-intercept (b) is 0 in this case, the relationship can be written as y = 83x + 0, or simply y = 83x.