Question

As a certain engine's rotation speed increases, its temperature increases at a constant rate. The table compares the engine's rotation speed (in cycles per second) and its temperature (in degrees Celsius).

Answer 1

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Answer:

15° Celsius.

Step-by-step explanation:

Begin by deriving an equation to represent the values in the table. Use the slope formula:

$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$

Plug in values from the table into the formula:

$m = \frac{27.0 - 22.2}{15-9}$

Simplify:

$m = \frac{4.8}{6}$

Reduces to:

m = 0.8. This is the slope of the equation.

Use a point from the table and plug it into the equation y = mx + b, along with the slope to calculate the y-intercept:

27 = 0.8(15) + b

27 = 12 + b

27 - 12 = b

b = 15. This represents the value when x = 0, therefore:

The engine's temperature at rest is 15° Celsius.