The function 56 - 4y = -5x can be used to determine the total amount of money, y, after money is added for x days. What is the rate of change in dollars with respect to the number of days?

Answer 1

That is the slope of the line described by

56 - 4y = -5x

-4y = -5x - 56

y = (5/4)x + 14

y = mx + b

m = slope = 5/4

Answer 2

56 - 4y = -5x, where y is is money and x is days. What is rate of change (slope) in y with respect to x?

You can drop the 56 now if you want, because we are only looking for slope. In y=mx+b, format, m is slope, and b is the intercept (which is not important for this question).

-4 y = -5 x - 56

y = 5/4 x + 14

The slope, rate of change, is 5/4. So, you will make 5 dollars every 4 days.