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### Course: Grade 8 (Virginia)>Unit 4

Lesson 10: Creating linear functions

# Linear functions word problem: paint

Sal is given a verbal description of a real-world relationship involving a person painting his room, and is asked to find the formula of the function that represents this relationship.

## Want to join the conversation?

• Why do we have to write, for example, A(t). Why can't we just write y? Isn't it the same thing? I am confused by what A of t means.
• I think that using y = mx + b, will turn it into a slope-intercept form of linear equation,
whereas using A(t) = mt + A(0) is a definition of a function..
hope that is clear
• Why would a(t) be how much he has left to paint? That kinda confused me during the video
• I think in this video we defined a function for the area left to paint, because it is the way to realistically “translate” the situation Hiro finds himself in.
We could have defined A(t) as the total area painted as a function of time. This would mean the greater the input time, the greater the output (painted area).
Yet it would not describe Hiro’s situation as accurately - at some point he will have painted his entire room - that’s why we defined the function the way we did - because it has a point which corresponds to the situation where the entire room is painted.
• The fact that immediately after reading the question, I thought
``A(t) = (28 + 8*3) - 8x``
was the answer, is the moment I felt a brief mastery of linear functions lol
• Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove to get to the safe zone at 24 meters per second. After 4 seconds of driving, she was 70 meters away from the safe zone.
Let D(t), denote the distance to the safe zone D (measured in meters) as a function of time t (measured in seconds).
Write the function's formula.
D(t)=

Can anyone help me with this? I don't know how to build the function. Thanks in advance...
• I think the " 70 meters away from the safe zone" means "70m left to drive to the safe zone".So:
distance to safe zone = 24*4+70 = 166
the function should be D=166-24t. She needs to drive 166m, and she approaches the safe zone at 24m/s means her distance to safe zone is reducing by 24m/s, so it's -24t, not 24t
• Could I put the solution in Y=mx+b as A(t)=-8t+52
• I still don't understand what the function formula is because my question is nothing like this.
• Why do all this?
• do people in real life actually think about formulas for painting a room. Way to complicated for nothing.
• What is the constant of proportionality in the equation y = 7x. Is it just 7?
• Yes, the 7 is the constant of proportionality.
• can the formula be also: A(t)= 52-8t ?
• Yes! Since subtraction and addition are both commutative, -8t+52 can also be written as 52-8t.