Answer: [tex]A(t)=-8t+52[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
According to the data given in the exercise, you know that:
- [tex]A(t)[/tex] represents the area to paint the Hiros' romm as a function of time.
- The rate he painted the room was 8 square meters per hour.
- The area left to paint after 3 hours was 28 m².
Therefore, based on this, you can idenfity that:
1. The slope of the line is:
[tex]m=-8[/tex]
2. One of the point on the line is:
[tex](3,28)[/tex]
So you must substitute the slope and the coordinates of that point into [tex]y=mx+b[/tex] and then solve for "b" in order to find its value:
[tex]28=-8(3)+b\\\\28+24=b\\\\b=52[/tex]
Therefore, you can determine that the function [tex]A(t)[/tex] is:
[tex]A(t)=-8t+52[/tex]
