Question

consider this table of values.
input | 0 | 1 | 2 | 3
output | 9 | 7 | 5 | 3
which of these graphs corresponds to the function shown in the table of values?
graphs w, x, y, z shown
a. x
b. w
c. z
d. y

Explanation:

Step1: Analyze the table

The table has inputs (x) 0, 1, 2, 3 and outputs (y) 9, 7, 5, 3. The slope \( m=\frac{7 - 9}{1 - 0}=- 2\), and the y - intercept (when \(x = 0\)) is 9. The equation of the line is \(y=-2x + 9\).

Step2: Check the y - intercept

For graph W, when \(x = 0\), \(y = 9\) (matches the y - intercept from the table). For graph X, the y - intercept is 4 (does not match). For graph Y, the y - intercept is 9 but the slope seems less steep (since the change in y for \(x\) from 0 to 1 is not - 2). For graph Z, the y - intercept is 9 but the slope is steeper (change in y for \(x\) from 0 to 1 is more than - 2).

Step3: Verify the slope

For graph W, when \(x\) increases by 1 (from 0 to 1), \(y\) decreases by 2 (from 9 to 7), which matches the slope \(m=-2\) calculated from the table. So graph W corresponds to the function in the table.

Answer:

B. W