If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 11: Constructing linear models for real-world relationships

# 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. • 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.
• 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
• I still don't understand what the function formula is because my question is nothing like this. • 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 represent the distance (in meters) from the safe zone after t seconds.
Complete the equation for the relationship between the distance and number of seconds.
D=,

I dont know where to start • Could I put the solution in Y=mx+b as A(t)=-8t+52 • What is the constant of proportionality in the equation y = 7x. Is it just 7? • I had one of these questions that was with no rate, and divided to figure it out, but it gave me an repeating decimal. Do I need to use what was previously taught to transform decimals into fractions or am I doing it wrong? • I'm confused, how do you know which variable to substitute? By that, I mean at why did Sal substitute A(0)=b=52, then at he substituted (the second variable t that comes up- it wouldn't let me bold it) A(t)=-8t+b?? • I think you need to review the lessons on working with linear equations. And, creating the equation for a line. Sal is creating the equation of the line. He is using slope intercept form to create the equation.
-- "m" = slope. Sal calculates the slope using the slope formula: (y2-y1)/(x2-x1), but in this case the variable is "t" rather than "x".
-- "b" is always the y-intercepts. That is a very specific point where the line crosses the y-axis. So, that point always has an x-value (in this problem it is a t-value) of 0. This is why Sal is using t=0. And, the table tells him if t=0, then the function's output=52. So, b=52.

Hope this helps. 