Answer:
0.5 hours
Step-by-step explanation:
The area-time table shows a linear relation between the variables (a same increment in one variable is related to the same increment in the other variable).
Slope (m) is determined with points (30, 2) and (45, 2.75):
m = (y2 - y1)/(x2 - x1) = (2.75 - 2)/(45 - 30) = 0.05
y-intercept is determined with point (30, 2) as follows:
y = mx + b
2 = 0.05(30) + b
b = 2 - 0.05(30) = 0.5
The y-intercept represents in this context the constant amount of time to clean up.
Natsumi will take 0.5 hours to clean up.
Let the area of the wall painted by Natsumi in 'x' hours and cleaning time 'b' is represented by the linear equation,
y = mx + b
Here, m = Time taken to paint 1 square meter of the wall
b = Time taken to clean up
If the linear graph of the linear equation passes through two points [tex](x_1,y_1)[/tex] and[tex](x_2,y_2)[/tex],
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table given in the question,
If two points are (30, 2) and (45, 2.75),
m = [tex]\frac{2.75-2}{45-30}[/tex]
m = [tex]\frac{0.75}{15}[/tex]
m = 0.05
Therefore, equation will be,
y = 0.05x + b
Graph of this equation passes through a point (60, 3.5),
3.5 = 0.05(60) + b
b = 3.5 - 3
b = 0.5 hours
Therefore, Natsumi will take 0.5 hours to clean up.
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