Math111i_GroupQuiz2_Solutions

# Math111i_GroupQuiz2_Solutions - form That follows as-2 x 7...

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Math 111I Sec 001 Group Quiz 2 Name Directions: Read each question carefully and answer in the space pro- vided. The use of calculators is allowed, but not necessary. There are 10 points possible. To receive partial credit on any problem work must be shown. 1. y is directly proportional to x , and when y = 17 . 4 we have that x = 6. A) Find a formula to describe y as a function of x . B) Use this formula to ﬁnd y when x is 8. Solutions. A) The deﬁnition to directly proportional tells us that our line looks like y = kx, or that the point (0 , 0) lies on our line. So we ﬁnd the equation of the line through (6 , 17 . 4) and (0 , 0) which follows as y = 17 . 4 6 x = 2 . 9 x. B) Now we have y = 2 . 9 x , or if we wanted to to express y as a function of x , y = f ( x ) = 2 . 9 x . Question B) asks us to compute f (8), and we do so to ﬁnd f (8) = 2 . 9(8) = 23 . 2 . 2. Determine whether the two lines are perpendicular - 2 x + 7 y = 9 and 8 x - 4 y = 9. Show your work and state whether they are perpendicular or not. Solutions. We begin by algebraically manipulating the two equations to y = mx + b

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Unformatted text preview: form. That follows as-2 x + 7 y = 9 7 y = 2 x + 9 y = 2 7 x + 9 7 , Math 111I Sec 001 Group Quiz 2 and 8 x-4 y = 9-4 y =-8 x + 9 y =-8-4 x-9 4 y = 2 x-9 4 . Now because 2 6 =-7 2 we have that our two lines cannot be perpendicular. 3. Determine whether the following data is linear. If it is linear, ﬁnd the function and write your answer in the form y = mx + b . If the data is not linear then state that. x y-5 8-4 5-3 2-2-1-7 Solutions. It is easy to compute the average rates of change for every interval m [-5 ,-4] ,m [-4 ,-3] ,m [-3 ,-2] , and m [-2 , 0] . For example m [-4 ,-3] = 5-2-4-(-3) =-3 . But more importantly the tricky value to compute is m [-2 , 0] =-1-(-7)-2-= 6-2 =-3 . So we have that our function is linear with a slope of m =-3, and we are given the y-intercept as (0 ,-7). Thus the equation of our line is y =-3 x-7 , and we are done....
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## This note was uploaded on 02/16/2011 for the course MATH 111 taught by Professor Hitchcock during the Fall '08 term at South Carolina.

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Math111i_GroupQuiz2_Solutions - form That follows as-2 x 7...

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