Function f is defined by f x = - a x + b , where a and b are constants.

Question

Function f is defined by f x = - a x + b , where a and b are constants. In the xy -plane, the graph of y = f x - 12 has a y- intercept at 0 , - 75 7 . The product of a and b is 320 7 . What is the value of a ?

Accepted Answer

The correct answer is 20 . It&rsquo;s given that f x = - a x + b . Substituting - a x + b for f x in the equation y = f x - 12 yields y = - a x + b - 12 . It&rsquo;s given that the y -intercept of the graph of y = f x - 12 is 0 , - 75 7 . Substituting 0 for x and - 75 7 for y in the equation y = - a x + b - 12 yields - 75 7 = - a 0 + b - 12 , which is equivalent to - 75 7 = - 1 + b - 12 , or - 75 7 = b - 13 . Adding 13 to both sides of this equation yields 16 7 = b . It&rsquo;s given that the product of a and b is 320 7 , or a b = 320 7 . Substituting 16 7 for b in this equation yields a 16 7 = 320 7 . Dividing both sides of this equation by 16 7 yields a = 20 .

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