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Determine whether the relationship shows a linear function. If so, write the function.

[ x: 1 , 2 , 3 , 4 , 5 ]
[ y: 9 , 6 , 3 , 0 , -3 ]

a) ( y = -3x + 12 )
b) ( y = 3x - 6 )
c) ( y = 2x - 3 )
d) None

1 Answer

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Final answer:

The relationship shown is a linear function with a constant rate of change, where y decreases by 3 as x increases by 1. The corresponding linear equation is y = -3x + 12, which is option (a) from the choices given.

Step-by-step explanation:

To determine whether the relationship shows a linear function and, if so, to write the function given the sets x: 1, 2, 3, 4, 5 and y: 9, 6, 3, 0, -3, we need to look for a constant rate of change. We notice that as x increases by 1, y decreases by 3. This is a constant rate of change which suggests a linear relationship. The slope (m) of the line would be -3 (the change in y for a unit change in x), and we need to find the y-intercept (b).

If we use the first coordinate pair (1, 9), we can substitute x and y into the linear equation format y = mx + b to find the y-intercept:

9 = (-3)(1) + b

b = 9 + 3

b = 12

So the linear equation that represents this relationship is y = -3x + 12, which corresponds to option (a).

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