Math worksheet for writing equations from tables, featuring sets A and B with answer banks.

Let me work through each table to find the equation that represents it.

Set A:

Table 1: x: 0, 2, 4 → y: -5, -1, 3
- Slope = (−1 − (−5))/(2 − 0) = 4/2 = 2
- y-intercept when x=0 is -5
- Equation: y = 2x − 5 → B

Check: x=4: y = 2(4) − 5 = 8 − 5 = 3 ✓

Table 2: x: 2, 4, 6 → y: 7, 13, 19
- Slope = (13 − 7)/(4 − 2) = 6/2 = 3
- Using point (2, 7): 7 = 3(2) + b → b = 1
- Equation: y = 3x + 1 → C

Check: x=6: y = 3(6) + 1 = 19 ✓

Table 3: x: -4, 2, 6 → y: -10, -1, 5
- Slope = (−1 − (−10))/(2 − (−4)) = 9/6 = 3/2
- Using point (2, -1): -1 = (3/2)(2) + b → -1 = 3 + b → b = -4
- Equation: y = (3/2)x − 4 → A

Check: x=-4: y = (3/2)(-4) − 4 = -6 − 4 = -10 ✓
Check: x=6: y = (3/2)(6) − 4 = 9 − 4 = 5 ✓

Set B:

Table 1: x: -4, 0, 4 → y: 7, 6, 5
- Slope = (6 − 7)/(0 − (−4)) = −1/4
- y-intercept when x=0 is 6
- Equation: y = −(1/4)x + 6 → D

Check: x=4: y = −(1/4)(4) + 6 = −1 + 6 = 5 ✓

Table 2: x: 3, 5, 7 → y: 1, -3, -7
- Slope = (−3 − 1)/(5 − 3) = −4/2 = −2
- Using point (3, 1): 1 = −2(3) + b → 1 = −6 + b → b = 7
- Equation: y = −2x + 7 → A

Check: x=7: y = −2(7) + 7 = −14 + 7 = −7 ✓

Table 3: x: -4, -3, 2 → y: -14, -10, 10
- Slope = (−10 − (−14))/(−3 − (−4)) = 4/1 = 4
- Using point (-4, -14): -14 = 4(-4) + b → -14 = -16 + b → b = 2
- Equation: y = 4x + 2 → C

Check: x=2: y = 4(2) + 2 = 10 ✓

Final Answer:
Set A: 1-B, 2-C, 3-A
Set B: 1-D, 2-A, 3-C