You test 8 automobiles of the same make and model and find their mileage ratings to be 27, 27, 28, 29, 32, 33, 34, and 1,000,000 mpg, arranged in order from smallest to largest. if you use inferential statistics (and reject the outlier) to predict what mileage consumers can expect when they buy this type of car, what value would you predict?

The statement " y varies directly as x ," means that when x increases,y increases by the same factor. In other words, y and x always have the same ratio:

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x , and y = 6 when x = 2 , the constant of variation is k =  = 3 . Thus, the equation describing this direct variation is y = 3x .

Example 1: If y varies directly as x , and x = 12 when y = 9 , what is the equation that describes this direct variation?

k =  =  
y =  x

Example 2: If y varies directly as x , and the constant of variation is k =  , what is y when x = 9 ?

y =  x = (9) = 15

As previously stated, k is constant for every point; i.e., the ratio between the y -coordinate of a point and the x -coordinate of a point is constant. Thus, given any two points (x 1, y 1) and (x 2, y 2) that satisfy the equation,  = k and  = k . Consequently,  =  for any two points that satisfy the equation.

Example 3: If y varies directly as x , and y = 15 when x = 10 , then what is y when x = 6 ?

 =  
 =  
6() = y 
y = 9

3

step-by-step explanation:

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