Which function has highest rate of change?
2x + 6y = 10 (or) Cost of 2 chocolates is 8 dollars.
Algebraic Function
Verbal Description
Both the functions
Neither of the functions
To determine which function has the highest rate of change, we need to compare the rate of change of both functions.
For the algebraic function 2x + 6y = 10:
- We can rewrite it as y = -1/3x + 5/3 in slope-intercept form.
- The slope, or rate of change, in this case, is -1/3.
- Therefore, the rate of change for this function is -1/3.
For the verbal description "Cost of 2 chocolates is 8 dollars":
- We can translate it into an algebraic function as 2c = 8, where c represents the cost of one chocolate.
- We can solve this equation to find that c = 4.
- However, this equation does not have a slope or rate of change since it is a single equation expressing a constant relationship.
Comparing the two functions, we can see that the algebraic function, 2x + 6y = 10, has a rate of change (-1/3) while the verbal description does not have a rate of change. Therefore, the function 2x + 6y = 10 has the highest rate of change.
To determine which function has the highest rate of change, we can analyze the slope of each function.
The given equation, 2x + 6y = 10, can be rewritten in slope-intercept form as y = (-1/3)x + 5/3. From this equation, we can see that the coefficient of x, which is -1/3, represents the slope of the line. Therefore, the slope of this function is -1/3.
On the other hand, the verbal description states that the cost of 2 chocolates is 8 dollars. This description does not provide any information about the rate of change, so we cannot determine the slope or rate of change from this verbal description.
Based on this analysis, the algebraic function, 2x + 6y = 10, has a defined rate of change (-1/3), whereas the verbal description does not provide any rate of change information. Thus, the algebraic function has the highest rate of change among the two options given.