Final answer:
The rate of change of y with respect to x of the equation 6x + 5y = 20 is -6/5. This represents the slope of the line, which is constant along the entire line, with a y-intercept at 4.
Step-by-step explanation:
The rate of change of y with respect to x in the equation 6x + 5y = 20 can be found by solving for y and then differentiating with respect to x. To express y explicitly, rearrange the equation to solve for y:
5y = 20 - 6x
y = (20/5) - (6/5)x
y = 4 - (6/5)x
Now, differentiate y with respect to x:
dy/dx = -6/5
The coefficient -6/5 represents the rate of change of y with respect to x, or the slope of the line. When the value of y changes as a function of x, a graph of this relationship can be plotted showing the slope as the rise over the run for every point on the line. In this case, the slope remains constant along the entire line, and the y-intercept is 4 (the point where the line crosses the y-axis).