Question

x | y
-2 | 1
-1 | 3
0 | 5
3 | 11
which equation could be used to generate the given table of values?
options:
y = 2x + 5
y = 5 - 2x
y = x + 3
y = 3x + 7

Explanation:

Step1: Test \( x = -2 \) in each equation

• For \( y = 2x + 5 \): \( y = 2(-2)+5 = -4 + 5 = 1 \) (matches the table's \( y = 1 \) when \( x=-2 \)).
• For \( y = 5 - 2x \): \( y = 5 - 2(-2)=5 + 4 = 9 \) (does not match \( y = 1 \)).
• For \( y = x + 3 \): \( y = -2 + 3 = 1 \) (matches here, but check another value).
• For \( y = 3x + 7 \): \( y = 3(-2)+7 = -6 + 7 = 1 \) (matches here, check another value).

Step2: Test \( x = -1 \) in remaining candidates

• For \( y = 2x + 5 \): \( y = 2(-1)+5 = -2 + 5 = 3 \) (matches table's \( y = 3 \) when \( x=-1 \)).
• For \( y = x + 3 \): \( y = -1 + 3 = 2 \) (does not match \( y = 3 \)).
• For \( y = 3x + 7 \): \( y = 3(-1)+7 = -3 + 7 = 4 \) (does not match \( y = 3 \)).

Step3: Confirm with \( x = 0 \)

• For \( y = 2x + 5 \): \( y = 2(0)+5 = 5 \) (matches table's \( y = 5 \) when \( x = 0 \)).

Answer:

\( y = 2x + 5 \)