Question

which sequence of y-values was formed from the function $y = -2x - 9$ using whole numbers for $x$?
a $-13, -15, -17, -19$
b $-13, -16, -19, -21$
c $-11, -20, -29, -38$
d $-10, -12, -14, -15$
e $16, 14, 12, 10, 8$

Explanation:

Step1: Recall the function and whole numbers

The function is \( y = -2x - 9 \), and \( x \) should be whole numbers (0, 1, 2, 3, ...). Let's find the difference between consecutive \( y \)-values. For a linear function \( y = mx + b \), the difference between consecutive \( y \)-values (when \( x \) increases by 1) is \( m \). Here, \( m=-2 \), so the difference between consecutive \( y \)-values should be -2 (or the absolute difference is 2, and each subsequent \( y \) is 2 less than the previous if \( x \) increases by 1, or 2 more if \( x \) decreases by 1, but since \( x \) is a whole number, we can check the sequences.

Step2: Analyze each option

• Option A: The sequence is -13, -15, -17, -19. Let's check the differences: \( -15 - (-13) = -2 \), \( -17 - (-15) = -2 \), \( -19 - (-17) = -2 \). The common difference is -2, which matches the slope of the function. Let's verify with \( x \) values. Let's find \( x \) for the first term: \( -2x - 9=-13 \Rightarrow -2x=-4 \Rightarrow x = 2 \). Then next \( x = 3 \): \( -2(3)-9=-6 - 9=-15 \), \( x = 4 \): \( -2(4)-9=-8 - 9=-17 \), \( x = 5 \): \( -2(5)-9=-10 - 9=-19 \). So \( x \) values are 2, 3, 4, 5 (whole numbers), which works.
• Option B: Sequence -13, -16, -19, -21. Differences: \( -16 - (-13)=-3 \), \( -19 - (-16)=-3 \), \( -21 - (-19)=-2 \). Not a constant difference of -2, so eliminate.
• Option C: Sequence -11, -20, -29, -38. Differences: \( -20 - (-11)=-9 \), \( -29 - (-20)=-9 \), \( -38 - (-29)=-9 \). Difference is -9, not -2, eliminate.
• Option D: Sequence -10, -12, -14, -15. Differences: \( -12 - (-10)=-2 \), \( -14 - (-12)=-2 \), \( -15 - (-14)=-1 \). Not a constant difference of -2 (last difference is -1), eliminate.
• Option E: Sequence 16, 14, 12, 10, 8. Let's check the function: If \( y = 16 \), then \( 16=-2x - 9 \Rightarrow -2x=25 \Rightarrow x=-12.5 \), not a whole number. Eliminate.

Answer:

A. -13, -15, -17, -19