A quality control technician is using a linear equation to monitor a machine's energy output. To verify if a specific data point from the machine's logs is a solution to the model, the technician substitutes the values into the equation. If the resulting mathematical statement is true (such as ${}10 = 10$), what is the correct conclusion about that data point?

A project manager is using a linear model to estimate the relationship between hours worked and total project cost. To verify if a specific data entry $(x, y)$ from a previous project is a solution to this linear cost equation, arrange the following procedural steps in the correct order.

An inventory manager is using a linear equation to predict warehouse capacity. To verify specific data entries, they must test ordered pairs $(x, y)$ in the equation. Match each mathematical outcome of this test with its corresponding interpretation.

In a professional cost-tracking model represented by a linear equation, if substituting the values of an ordered pair $(x, y)$ into the equation results in a false mathematical statement, then that data point is NOT a solution and will not lie on the graph of the line.

Audit of Energy Efficiency Records

An energy auditor is reviewing a facility's efficiency data modeled by the linear equation $y = 2x - 3$, where $x$ represents hours of operation and $y$ represents power consumption in kilowatts. To verify if a recorded data point $(x, y)$ is a valid solution, the auditor substitutes the values into the equation. If this substitution simplifies to a(n) ____ mathematical statement, the auditor concludes that the point is a solution and lies exactly on the line representing the equation.