Final answer:
The rate of change of y with respect to x in the equation 4x + 7y = 21 is -4/7.
Step-by-step explanation:
The rate of change of y with respect to x in the equation 4x + 7y = 21 can be found by solving the equation for y, which would give us a linear equation in the form y = mx + b, where m is the slope or rate of change. To isolate y, we subtract 4x from both sides of the equation and get 7y = -4x + 21. Dividing both sides by 7 to solve for y gives us y = (-4/7)x + 3. Hence, the slope of the line, which is the rate of change of y with respect to x, is -4/7.