Given the table for x, time in minutes and y, distance traveled:
x - time 4 3 10 7 9
y - distance 76 57 190 133 171
a. Every minute Response area meters are traveled.
b. Write an equation to show the relationship between x and y. Response area
c. This relationship is Response area because the y-intercept is Response area .
a. Every minute 19 meters are traveled.
b. The equation to show the relationship between x and y is y = 19x.
c. This relationship is a linear relationship because the y-intercept is 0.
Given the table for x, time in minutes and y, distance traveled:
x - time 4 3 10 7 9
y - distance 76 57 190 133 171
a. Every minute Response area meters are traveled.
b. Write an equation to show the relationship between x and y. Response area
c. This relationship is Response area because the y-intercept is Response area .
a. Every minute 19 meters are traveled.
b. The equation to show the relationship between x and y is y = 19x - 19.
c. This relationship is linear because the y-intercept is -19.
a. To find the distance traveled per minute, we can calculate the rate of change of the distance over time.
For the first pair of values (4 minutes and 76 meters), the distance traveled per minute would be 76 divided by 4, which is 19 meters per minute. Similarly, for the second pair (3 minutes and 57 meters), the distance traveled per minute would be 57 divided by 3, which is 19 meters per minute as well.
We can calculate the distance traveled per minute for each pair and find the average value.
(19 + 63.33 + 19 + 19 + 38.33) / 5 = 31.13 meters per minute
Therefore, every minute, approximately 31.13 meters are traveled.
b. To write an equation to show the relationship between x and y, we can use the formula for a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope, we can use any two points from the table. Let's use the points (4, 76) and (10, 190):
slope (m) = (y2 - y1) / (x2 - x1)
= (190 - 76) / (10 - 4)
= 114 / 6
= 19
Now, let's find the y-intercept (b) by substituting the slope and one of the points into the equation. Let's use the point (4, 76):
y = mx + b
76 = 19 * 4 + b
76 = 76 + b
b = 0
Therefore, the equation that shows the relationship between x and y is y = 19x.
c. This relationship is a linear relationship because the equation is in the form y = mx + b, where m is the slope and b is the y-intercept. The y-intercept (b) in this case is 0, which means that the distance traveled (y) starts from 0 when time (x) is 0.
a. To find out how many meters are traveled every minute, we can calculate the rates of change of the distance traveled per unit time. We can do this by finding the difference in distance between two consecutive time values and dividing it by the difference in time between those points.
Let's calculate the rates of change for each pair of consecutive points:
For (4, 76) and (3, 57) - The change in distance is 76 - 57 = 19 meters, and the change in time is 4 - 3 = 1 minute. So the rate of change is 19 meters / 1 minute = 19 meters/minute.
For (10, 190) and (7, 133) - The change in distance is 190 - 133 = 57 meters, and the change in time is 10 - 7 = 3 minutes. So the rate of change is 57 meters / 3 minutes = 19 meters/minute.
For (7, 133) and (9, 171) - The change in distance is 171 - 133 = 38 meters, and the change in time is 9 - 7 = 2 minutes. So the rate of change is 38 meters / 2 minutes = 19 meters/minute.
Since the rates of change are the same for all three pairs of consecutive points, we can conclude that the meters traveled every minute is 19 meters.
b. To find the equation that represents the relationship between x and y, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line.
We can choose any point from the given data. Let's choose (4,76):
Using the slope calculated in part a, which is 19, and the chosen point (4, 76), we can substitute these values into the point-slope form:
y - 76 = 19(x - 4).
Now we can simplify this equation:
y - 76 = 19x - 76.
Adding 76 to both sides of the equation:
y = 19x.
So the equation that represents the relationship between x and y is y = 19x.
c. The relationship between x and y is a linear relationship because the equation y = 19x represents a straight line on a graph. The y-intercept is 0, meaning that when x is 0, the distance traveled is also 0.