given table for x, time in minutes and y, distance traveled in meter
x - time (minutes) | 8 | 5 | 7 | 2 | 9 |
y - distance (meters) | 40 | 25 | 35 | 10 | 45 |
1. write an equation to show the relationship between x and y ______
2. The relationship is ______ because the y-intercept is _____
A. proportional
B. non proportional
C. non linear
1. To find the equation that shows the relationship between x and y, we can examine the data provided. We notice that when x is equal to 8, y is equal to 40. Similarly, when x is equal to 5, y is equal to 25. We can assume that there is a linear relationship between x and y.
To find the equation of this line, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) using two points (8, 40) and (5, 25):
m = (y2 - y1) / (x2 - x1)
m = (25 - 40) / (5 - 8)
m = -15 / -3
m = 5
Now, we can find the y-intercept (b) by substituting the slope and one of the points into the equation:
y = mx + b
25 = 5(5) + b
25 = 25 + b
b = 0
So, the equation that shows the relationship between x and y is y = 5x.
2. The relationship is A. proportional because the equation y = 5x represents a straight line passing through the origin (0, 0). The y-intercept is 0, indicating that when x is 0, y is also 0. This indicates a proportional relationship where the ratio between x and y is constant.
1. To show the relationship between x and y, we can use the equation of a line, which is in the form y = mx + b. In this case, "m" represents the slope and "b" represents the y-intercept.
To find the equation, we need to determine the values of "m" and "b". We can choose any two data points from the table and substitute their corresponding values into the equation to solve for those variables. Let's use points (2, 10) and (5, 25):
Using the point (2, 10):
10 = (2)m + b
Using the point (5, 25):
25 = (5)m + b
Now, we have a system of equations that we can solve to find the values of "m" and "b".
By subtracting the first equation from the second equation, we get:
25 - 10 = (5)m - (2)m + b - b
15 = 3m
Dividing both sides by 3, we get:
m = 5
Substituting this value back into one of the original equations:
10 = (2)(5) + b
10 = 10 + b
Subtracting 10 from both sides, we get:
b = 0
Therefore, the equation that shows the relationship between x and y is:
y = 5x
2. The relationship is proportional because the y-intercept is 0.
1. To find the equation that represents the relationship between x (time) and y (distance), we need to first identify the pattern. From the given data, we can see that as x increases, y also increases.
To determine the equation, we can start by looking for a general form that relates x and y. Let's assume it is a linear equation of the form y = mx + c, where m is the slope and c is the y-intercept. We can find the values of m and c by using any two points from the table.
For example, let's use the points (2, 10) and (5, 25). By substituting the values into the equation, we can solve for m and c:
10 = 2m + c ... (1)
25 = 5m + c ... (2)
Solving this system of equations, we can find the values of m and c. Subtracting equation (1) from equation (2), we get:
(25 - 10) = (5m + c) - (2m + c)
15 = 3m
Dividing both sides by 3, we find that m = 5. Substituting this value of m into equation (1), we can find c:
10 = 2(5) + c
10 = 10 + c
c = 0
Therefore, the equation that represents the relationship between x and y is y = 5x + 0. Simplifying further, we have y = 5x.
2. Now, let's analyze the relationship based on the y-intercept value (c) from the equation y = 5x + c. In this case, the y-intercept is 0, which means the line passes through the origin (0, 0).
Since the y-intercept is 0, we can conclude that the relationship is proportional. In a proportional relationship, the y-intercept is always 0, indicating that the value of y is directly proportional to x.
So, the answer is:
A. proportional