Answer:
The relationship between the input and output variables in the given table of values are;
Question 1
Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
x; 1, 2, 3, 4, 5
y; 140, 280, 420, 560
Question 3
No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent
Question 4
No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3
Question 5
Yes, it is a proportional relationship because it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned
Question 7
Yes because the ratio of the miles per hour are all equivalent to 1.75
What is a proportional relationship?
A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.
Question 1
A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant
Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12
Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
The points on the graph are;
(0, 0), (5, 700), (6, 840), (7, 980)
Therefore;
y = (5/700)•x = (1/140)•x
The table is therefore;
x; 1, 2, 3, 4
y; 140 280 420 560
Question 3;
The ratio of the dozens of cookies to cups of flour, gives;
Recipe 1; R = 2/1.5 dozen per cup of flour
Which gives;
Approximately 1.33 dozens per cup of flour
Recipe 2, R = 3/3 dozens per cup of flour
Which gives;
Recipe 3, R = 4/4.5 dozens per cup of flour
Therefore;
No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent
Question 4
The ratio of the terms are;
18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3
Therefore;
No it is not proportional because 18.26/36.5 is not equal 21.1/63.3
Question 5
Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;
Yes, it is a proportional relationship because, it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned
Question 7
The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75
Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75
Explanation: