unit 3 lesson 11 graphing
given the table for x, lawns mowed and y, money earned:
x-# of lawns 7 6 2 9 3
y-$ earned 294 252 84 378 126
a. every lawn mowed is _ dollars earned.
b. dollars/1lawn mowed is called a _
c. this relationship is _ because _ tickets sold is $0 earned.
non proportional variable unit rate proprotional decreasing 1 84 42 0 5 non linear
a. every lawn mowed is 42 dollars earned.
b. dollars/1 lawn mowed is called a unit rate.
c. This relationship is non-proportional because 0 lawns mowed is $0 earned.
To answer these questions, we need to understand the relationship between the number of lawns mowed and the amount of money earned based on the given table.
a. To find how many dollars are earned for every lawn mowed, we can calculate the unit rate. The unit rate is obtained by dividing the total dollars earned by the total number of lawns mowed.
Total dollars earned = $294 + $252 + $84 + $378 + $126 = $1134
Total number of lawns mowed = 7 + 6 + 2 + 9 + 3 = 27
Unit rate = Total dollars earned / Total number of lawns mowed
Unit rate = $1134 / 27
By performing the calculation, you should find that the unit rate is approximately $42. Therefore, every lawn mowed is $42 earned.
b. The term for dollars per one lawn mowed is called the "unit rate." In this case, the unit rate is $42 per lawn mowed.
c. Based on the given table, the relationship between the number of lawns mowed and the amount of money earned is non-proportional. This is because the values in the table do not have a constant ratio. In a proportional relationship, the ratio between the two variables would remain the same for every value.
Furthermore, this relationship is decreasing because as the number of lawns mowed decreases, the amount of money earned also decreases. This can be observed in the table: as x decreases from 9 to 2, y decreases from $378 to $84.
It is also worth noting that this relationship is non-linear since the graph of these data points would not be a straight line.
a. To find the dollar amount earned per lawn mowed, we can calculate the ratio of the money earned to the number of lawns mowed for each data point.
For the first data point (7 lawns mowed, $294 earned):
Dollars earned per lawn mowed = 294/7 = $42
For the second data point (6 lawns mowed, $252 earned):
Dollars earned per lawn mowed = 252/6 = $42
For the third data point (2 lawns mowed, $84 earned):
Dollars earned per lawn mowed = 84/2 = $42
For the fourth data point (9 lawns mowed, $378 earned):
Dollars earned per lawn mowed = 378/9 = $42
For the fifth data point (3 lawns mowed, $126 earned):
Dollars earned per lawn mowed = 126/3 = $42
Therefore, every lawn mowed is $42 dollars earned.
b. Dollars/1 lawn mowed is called a unit rate.
c. This relationship is non-proportional because the ratio of dollars earned to lawns mowed is not constant. For example, with 0 lawns mowed, $0 is earned, and with 5 lawns mowed, $84 is earned, indicating a non-linear relationship.
Overall, we can conclude that the dollars earned for mowing lawns is non-proportional, with a unit rate of $42 per lawn mowed.