Which situation could NOT represent a proportional relationship?
1 answer:
Answer:
The weight in x weeks of a puppy that gains 2 pounds per week if it starting weight is 8 pounds.
Step-by-step explanation:
Given:
A proportional relationship is one in which one variable varies directly with the other. Let the dependent variable be y and independent variable be y.
If y is directly proportional to x, then,
, where, k is a constant of proportionality.
Now, let us check each option and try to express a relationship between them.
Option 1:
The weight in weeks of a puppy that gains 2 pounds per week if it starting weight is 8 pounds.
Let the weight be represented by . Initial weight is 8 pounds.
Weight gain per week is 2 pounds. So, weight gain in weeks is
.
Therefore, total weight is,
This is a linear relationship but not a proportional relationship as it is not of the form . So, option 1 could NOT represent a proportional relationship.
Option 2:
Cost of purchasing 1 pound of bananas is $ 0.55. So, cost of purchasing pounds of bananas will be
. It is of the form
. So, it represents a proportional relationship.
Option 3:
Number of gallons of water in 1 barrel is 50. So, number of gallons in barrels will be
. It is of the form
. So, it represents a proportional relationship.
Option 4:
Amount earned by an employee in 1 hour is $ 9.25. So, amount earned in hours will be
. It is of the form
. So, it represents a proportional relationship.
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Answer:
- distance to x-axis: 3 units
- distance to y-axis: 2 units
- the reflected point is (2, 3)
Step-by-step explanation:
The given point is (-2, 3), labeled point A in the attachment.
As you know, the distance from the x-axis is given by the y-coordinate. Here, that distance is ...
3 units from the x-axis
__
The distance from the y-axis is given by the magnitude of the x-coordinate. Here, that distance is ...
2 units from the y-axis
Note that the negative coordinate value means the point is located that distance to the left of the y-axis.
__
Reflecting the point across the y-axis means choosing a point that is the same distance (2 units) right of the axis instead of left of the axis. The sign of the x-coordinate value will be positive, instead of negative. (The y-coordinate remains unchanged,)
__
The reflected point is (2, 3).
_____
<em>Additional comment</em>
As we have seen, reflection across the y-axis changes the sign of the x-coordinate:
(x, y) ⇒ (-x, y) . . . . reflection across the y-axis
Similarly, reflection across the x-axis changes the sigh of the y-coordinate:
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
