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Answered

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3.
Is the relationship shown by the data linear? If so, model the data with an equation.


x
y
–9
–2
–5
–7
–1
–12
3
–17


A. The relationship is not linear.

B. The relationship is linear; y + 9 = -4/5 (x + 2).

C. The relationship is linear; y + 2 = -5/4 (x + 9).

D. The relationship is linear; y + 2 = 4/5 (x + 9).

Sagot :

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Answer:

C.    The relationship is linear; y + 2 = (-5/4)x - 11.25

Step-by-step explanation:

If the relationship f is linear then its graph is a line D of equation y = ax+b

(-9 ,-2)∈D ⇔ -2 = -9a + b  (1)

(-5 , -7)∈D ⇔ -7 = -5a + b (2)

(2)-(1)⇒ -5 = 4a ⇒ a = -5/4

-2 = -9a + b  ⇒ -2 = -9(-5/4) + b ⇒  2 +45/4 = -b ⇒ b = -13.25

then

D : y = (-5/4)x - 13.25 ⇒ y + 2 = (-5/4)x - 11.25

since (-1,-12) and (3,-17) are points of D (easy to check)

then it’s a linear relationship

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