Which function has highest rate of change?
2x + 6y = 10 (or) Cost of 2 chocolates is 8 dollars.
The first function, 2x + 6y = 10, has a higher rate of change because it is a linear equation with variables x and y, while the second statement is describing a fixed cost for a fixed quantity of chocolates.
To determine which function has the highest rate of change, we need to compare the rate of change of each function. The rate of change of a function can be found by calculating the slope of the line representing the function.
Let's start by finding the slope of the line represented by the equation 2x + 6y = 10.
First, rewrite the equation in slope-intercept form (y = mx + b) by isolating the y variable:
2x + 6y = 10
6y = -2x + 10
y = (-2/6)x + 10/6
y = (-1/3)x + 5/3
Now we can see that the slope of the line is -1/3. This means that for every 1 unit change in x, y will change by -1/3 units.
Next, let's consider the cost of 2 chocolates being 8 dollars.
The cost of 2 chocolates is a fixed value, so there is no rate of change associated with it. Therefore, we cannot compare the rate of change of the cost of chocolates with the rate of change of the linear function.
Therefore, the function 2x + 6y = 10 has a rate of change of -1/3, whereas the cost of 2 chocolates being 8 dollars does not have a rate of change.
Therefore, the function 2x + 6y = 10 has the highest rate of change.