A technician is monitoring the pressure in a cooling system. The pressure decreases at a constant rate of 9 units per hour, and the initial pressure at the start of the observation (hour 0) is 4 units below the reference baseline. If this relationship is modeled by a line with a slope of $m = -9$ and a $y$-intercept of $(0, -4)$, which equation correctly represents the pressure $y$ after $x$ hours?

A facilities manager is monitoring the temperature in a cooling unit that is malfunctioning. The temperature is dropping at a constant rate of ${}9$ degrees per hour. At the start of the observation (hour ${}0$), the temperature is already ${}4$ degrees below the safety threshold. Arrange the following steps in the correct order to determine the linear equation in slope-intercept form ($y = mx + b$) that models this temperature change.

In a corporate budget model, a project's account balance is decreasing at a constant rate of 9 units per month (slope $m = -9$). At the start of the fiscal year (month 0), the account was already 4 units below the target baseline ($y$-intercept of $(0, -4)$). The linear equation in slope-intercept form that models this budget balance over time is $y = -9x - 4$.

In a civil engineering project, a drainage pipe's elevation relative to a reference baseline is modeled by a linear equation. The pipe's elevation decreases at a constant rate of 9 units per horizontal meter (slope $m = -9$). At the starting point (meter 0), the pipe's elevation is already 4 units below the reference baseline ($y$-intercept of $(0, -4)$). Match each component of this linear model to its correct mathematical representation.

Server Storage Capacity Model

Configuring the Deficit Tracker

A corporate logistics planner is setting up a deficit-tracking model for warehouse inventory. At the start of the observation (day ${}0$), the warehouse's stock level of a critical manufacturing component is already ${}4$ units below the optimal safety threshold (representing a $y$-intercept of $(0, -4)$). Due to daily production demand, the stock level decreases at a constant rate of ${}9$ units per day (representing a slope of $-9$).

To automate the tracking spreadsheet, the planner recalls the slope-intercept form, $y = mx + b$, and substitutes these values to find the final simplified equation of the line modeling the stock status $y$ over $x$ days.

Enter the final simplified linear equation in the blank below (you may write the full equation starting with $y =$ or just the simplified right-hand side expression):