Interpreting the zero of a linear function in a real world problem (IMRA 2026 publisher-initiated change)
About this video
A phone battery starts at 40% and drains 5% per hour, modelled by f(x) = -5x + 40. The video finds the zero of this function, x = 8, where the graph meets the x-axis, and interprets it: the battery dies after exactly 8 hours.
You'll be able to
- find the zero of a linear function from its graph.
- explain what the zero of a function means in a real-world situation.
- connect the starting value and rate of change in a story to the y-intercept and slope.
Key words
- zero of a function
- The x-value that makes the function equal 0; where the graph crosses the x-axis.
- rate
- How fast something changes, like 5% per hour.
- model
- A function that describes a real situation using maths.
Transcript
- [Instructor] A phone's battery is at 40% and drains at a steady rate of 5% per hour while playing music. The function f of x = -5x + 40 models the battery level as a percent where x is time in hours. What is the zero of this function and what does it mean in this situation?
Pause the video, try to figure that out. Okay, so this is the graph. Let me make sure you can see my writing. This is the graph of y = f of x, where f of x = -5x + 40. We can see that right when we start, the battery is at 40%. That's what they told us, the battery is at 40%, and drains at a steady state of 5% per hour.
And you can see every hour that goes by, the battery has gone down by 5%. Every hour that goes by, the battery has gone down by 5%. When they're talking about the zero of this function, they're really saying, "Okay, where does this function intersect the x-axis?
When does y = zero?" So we have this point right over here, this is the 8,0. And what this is saying is, is that after eight hours, or eight hours is exactly where the phone's battery has completely died. So that's what it means in this situation. Or actually just answer the first part, what is the zero of this function?
The zero of this function happens at when the number of hours is equal to eight or if we said that this was the x-axis, we would say x = 8, say this is the y-axis there. And then that way you would interpret that is it means that the battery dies at exactly eight hours.
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