Answer:
The temperature at rest is 15 degrees Celsius.
Step-by-step explanation:
The situation can be modeled by a linear equation of the form
[tex]y =mx+b[/tex].
The engine is at rest when its rotational speed is zero. To find what the temperature of the engine at rest is, we first need to find the increase in temperature for each increase in rotational speed, i.e. we need the slope of the graph that the table represents.
The slope is rise/run: and we evaluate it between the first two points:
[tex]m = \dfrac{25.4-23.8}{13-11} = 0.8[/tex]
Thus, the linear equation becomes
[tex]y = 0.8x+b[/tex]
and we find be from the first point [tex](11, 23.8)[/tex] as follows:
[tex]23.8 = 0.8(11)+b[/tex]
[tex]23.8 = 8.8+b[/tex]
[tex]b = 15[/tex]
which gives
[tex]\boxed{y =0.8x+b.}[/tex]
Thus, the temperature [tex]y[/tex] of the engine when it is a rest( i.e [tex]x =0[/tex]) is
[tex]y = 0.8(0)+15[/tex]
[tex]y =15.[/tex]
The temperature at rest is 15 degrees Celsius.
