Answer :
Solution:
Graph of temperature of a room(°F) and time(T) is given in the graph.
When Time increases temperature of a room also increases.
It means time is in directly proportional to temperature.
We can Find equation of line using two point slope formula.
The line passes through (0,65) and (20,75).
X coordinate = Time, Y coordinate = Temperature
Equation of line passing through [tex](x_{1}, y_{1}) {\text{and} (x_{2},y_{2}) {\text{is given by} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{x-x_{1}}[/tex]
Equation of line passing through (0,65) and (20,75) is given as:
⇒ [tex]\frac{y-65}{x-0}=\frac{75-65}{20-0}\\\\2 y -130=x\\\\ x -2 y +130=0[/tex]
When t=1 i.e x=1
1 - 2 y + 130 = 0
2 y = 131
y = 65.5°F
The temperature increases by 0.5° C with every increase of time by 1 minute.
The amount of temperature in °F, that increase by every 1 min is: 0.5.
Recall:
Slope (m) = rise / run = change in y / change in x.
Given the graph that represents the temperature of a room over time, to calculate how many °F the room's temperature increases by every 1 min, find the slope of the graph.
Slope of the graph using two points, (0, 65) and (20, 75):
Change in y (rise) = 75 - 65 = 10
Change in x (run) = 20 - 0 = 20
Slope (m) = 10/20 = 0.5
Therefore, the amount of temperature in °F, that increase by every 1 min is: 0.5.
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