An environmental engineer is monitoring the water level in a reservoir during a drought. The water level decreases at a constant rate of 2 feet every 5 days, which is represented by a slope of -rac{2}{5}. On day 10 of the study, the water level is recorded at $-5$ feet relative to the baseline. Which of the following linear equations in slope-intercept form correctly models the water level ($y$) over time ($x$) based on this data?

A quality control technician is documenting the concentration of a stabilizer in a chemical batch. The concentration decreases at a constant rate of -rac{2}{5} units per hour. At the 10-hour mark, the concentration level is recorded at -5 units relative to the target baseline. Arrange the following steps in the correct order to derive the slope-intercept equation y = -rac{2}{5}x - 1 for this process.

A small business owner is calculating the depreciation of a delivery van. The van's value decreases at a constant rate of -rac{2}{5} thousand dollars per year (m = -rac{2}{5}). At year 10, the value relative to the purchase price is -5 thousand dollars. After substituting these values into the point-slope formula and simplifying to the slope-intercept form $y = mx + b$, the value of the y-intercept ($b$) is ____.

A facility manager is tracking the reduction in available storage space as new machinery is installed. The storage space decreases at a constant rate of 2 cubic meters for every 5 machines added (slope $m = -\frac{2}{5}$). When 10 machines are installed, the available space is -5 cubic meters relative to the safety baseline. Match each step of the manager's calculation with the correct mathematical expression used to find the final equation for the storage space ($y$) based on the number of machines ($x$).

Deriving a Financial Model Equation

An inventory manager tracks the depletion of warehouse supplies. The supplies decrease at a constant rate, represented by a slope of $m = -\frac{2}{5}$. On day 10, the inventory level is -5 units relative to the safety stock threshold, giving the data point $(10, -5)$.

True or False: When recalling the point-slope formula to begin writing the equation of this line, the correct initial substitution is $y - 5 = -\frac{2}{5}(x - 10)$.

Surplus Inventory Clearance Tracking