Q:

Sven investigates the amount of damage to the head gaskets on the trucks in his fleet and find that the damage index depends on the ambient temperature. He develops the equation y = - 2 3 x + 14 to model the relationship. What does 14 mean? A) The temperature only adds 14 to the damage index. B) If there is no damage index then the ambient temperature is 14. C) If the damage index is 0, then the ambient temperature would be 0. D) If the ambient temperature is 0 then the damage index would be 14.

Accepted Solution

A:
Given is the damage index equation, [tex] y=\frac{-2}{3} x+14 [/tex] where y represents damage index, and x represents ambient temperature.It is similar to slope-intercept form of linear equation given by y = mx + b.Where m is said to be the slope of line and b is the y-intercept of the line. When x = 0, y = b.Similarly, if plug x = 0 in the damage index equation, [tex] y=\frac{-2}{3} (0)+14=14 [/tex] So, If ambient temperature, x = 0. Then damage index, y = 14. Hence, option D is correct i.e. " If the ambient temperature is 0 then the damage index would be 14".