Question

match the equation with the appropriate table of values.

tables of values (three tables with x and y columns) and equations: ( y = -2x + 2 ), ( y = 5x + 2 ), ( y = \frac{5}{2}x + 2 ), ( y = -3x + 2 )

Explanation:

Step1: Analyze \( y = -2x + 2 \)

Substitute \( x = -1 \): \( y=-2(-1)+2 = 4 \). \( x = 0 \): \( y = 2 \). \( x = 1 \): \( y=0 \). \( x = 2 \): \( y=-2 \). Matches first table.

Step2: Analyze \( y = 5x + 2 \)

Substitute \( x = -1 \): \( y=-5 + 2=-3 \). \( x = 0 \): \( y = 2 \). \( x = 1 \): \( y = 7 \). \( x = 2 \): \( y = 12 \). Matches second table.

Step3: Analyze \( y=\frac{5}{2}x + 2 \)

Substitute \( x=-2 \): \( y=\frac{5}{2}(-2)+2=-3 \). \( x = 0 \): \( y = 2 \). \( x = 2 \): \( y = 7 \). \( x = 4 \): \( y = 12 \). Matches third table.

Step4: Analyze \( y=-3x + 2 \)

Check \( x=-1 \): \( y = 3 + 2 = 5 \) (no table matches, so focus on the three equations above).

Answer:

• \( y = -2x + 2 \) matches the first table (x: -1, 0, 1, 2; y: 4, 2, 0, -2).
• \( y = 5x + 2 \) matches the second table (x: -1, 0, 1, 2; y: -3, 2, 7, 12).
• \( y=\frac{5}{2}x + 2 \) matches the third table (x: -2, 0, 2, 4; y: -3, 2, 7, 12).
• \( y = -3x + 2 \) does not match any shown tables (based on given x - values).