Math  /  Algebra

QuestionExamine the input-output table, which contains some of the ordered pairs of a linear function. \begin{tabular}{|c|c|} \hline Input (x)(x) & Output (y)(y) \\ \hline-4 & 4 \\ \hline-2 & 1 \\ \hline 0 & -2 \\ \hline 4 & -5 \\ \hline \end{tabular}
What is the initial value of the function? 4-4 2-2 0 4

Studdy Solution

STEP 1

1. The function is linear.
2. The initial value of the function is the y-intercept, which is the output when the input x=0 x = 0 .

STEP 2

1. Identify the y-intercept from the table.
2. Verify the y-intercept is consistent with the linearity of the function.

STEP 3

The y-intercept of a linear function is the output value when the input x=0 x = 0 .
From the table, when x=0 x = 0 , y=2 y = -2 .

STEP 4

Since the function is linear, the y-intercept should be consistent across the table.
Verify that the change in y y over the change in x x is constant.
For example, from (4,4) (-4, 4) to (2,1) (-2, 1) , the change in y y is 14=3 1 - 4 = -3 and the change in x x is 2(4)=2 -2 - (-4) = 2 .
The slope m=32 m = \frac{-3}{2} .
Verify this slope with another pair, from (2,1) (-2, 1) to (0,2) (0, -2) , the change in y y is 21=3 -2 - 1 = -3 and the change in x x is 0(2)=2 0 - (-2) = 2 .
The slope m=32 m = \frac{-3}{2} , consistent with the previous calculation.
The initial value of the function is:
2 \boxed{-2}

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