Hideki is draining a 45-gallon aquarium at a rate of 15 gallons per minute. What is the initial value of the linear function that represents this situation?

Question

kittybasil · Answer

Total: 45 gallons.
Rate: 15 gallons/minute, or $-15x$ where $x$ is the number of minutes passed. The reason it's negative is because the function is going downwards.

The linear function form that applies here would be $y=mx+b$ with $b$ being the y-intercept $45$. Your $m$ is already given as $-15$, so the function should be$$y=-15x+45$$

kittybasil · Answer

Oops, I didn't explain the negative part clearly. So basically the $mx$ part has a negative sign because the $\text{slope}$ is negative for a downwards-approaching linear function. Imagine it being like a slide versus a ladder, with up being positive values and down being negative values. Here, the function resembles a slide, so it's negative.