Final answer:
The rate of change for the function represented by the equation 4x - 2y = 6 is 2 boxes per minute. This is found by rearranging the equation to the form y = 2x - 3, which exposes the slope, or the rate of change, as 2.
Step-by-step explanation:
The equation given represents a linear function where y is the amount of boxes a worker can produce in a minute, x. The equation provided is 4x - 2y = 6. To find the rate of change, we need to solve this equation for y and then determine the slope of the resulting linear function.
First, we isolate y:
- 4x - 2y = 6
- 2y = 4x - 6
- y = 2x - 3
The slope-intercept form of a linear equation is y = mx + b, where m is the slope, and b is the y-intercept. Comparing our equation to the slope-intercept form, we see that the slope m is 2, which is the coefficient of x. Therefore, the rate of change of this function is 2 boxes per minute.