Math worksheet for determining linear equations from tables, with solutions and correctness checks.

We are given three problems in Set C, each with a table of (x, y) values and a proposed linear equation. We must check whether the proposed answer is correct or incorrect.

A linear equation has the form:
y = mx + b, where
- *m* is the slope: $ m = \frac{y_2 - y_1}{x_2 - x_1} $ (same for any two points),
- *b* is the y-intercept (value of y when x = 0).

Let’s verify each one carefully.

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Problem 1 (Set C)

Table:
| x | y |
|----|----|
| -6 | -12 |
| -3 | -7 |
| 0 | -2 |

Proposed answer: y = (5/3)x − 2

Step 1: Find slope using two points. Use (−6, −12) and (0, −2):
$ m = \frac{-2 - (-12)}{0 - (-6)} = \frac{10}{6} = \frac{5}{3} $ ✔ matches proposed slope.

Step 2: y-intercept: when x = 0, y = −2 → so b = −2 ✔ matches.

Check with third point (−3, −7):
Plug into y = (5/3)x − 2:
$ y = \frac{5}{3}(-3) - 2 = -5 - 2 = -7 $ ✔ matches.

So this proposed answer is Correct.

But in the image, it's marked as Incorrect (red X). That suggests the student made an error — but our calculation shows it's actually correct.

Wait — let’s double-check the table again:

Given:
x = −6 → y = −12
x = −3 → y = −7
x = 0 → y = −2

From x = −6 to x = −3: Δx = 3, Δy = (−7) − (−12) = 5 → slope = 5/3
From x = −3 to x = 0: Δx = 3, Δy = (−2) − (−7) = 5 → slope = 5/3
Consistent.

Equation: y = (5/3)x + b
Use (0, −2): −2 = (5/3)(0) + b → b = −2
So y = (5/3)x − 2 ✔️

✔ Correct.

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Problem 2 (Set C)

Table:
| x | y |
|---|---|
| 4 | −1 |
| 6 | 0 |
| 8 | 1 |

Proposed answer: y = (1/2)x − 3

Step 1: Slope using (4, −1) and (6, 0):
$ m = \frac{0 - (-1)}{6 - 4} = \frac{1}{2} $ ✔

Step 2: Find b using point (6, 0):
0 = (1/2)(6) + b → 0 = 3 + b → b = −3 ✔

Check with (8, 1):
y = (1/2)(8) − 3 = 4 − 3 = 1 ✔

Also check (4, −1):
(1/2)(4) − 3 = 2 − 3 = −1 ✔

So this is also Correct.

But in the image, it’s marked Incorrect. Again, likely student error.

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Problem 3 (Set C)

Table:
| x | y |
|---|---|
| −1 | 12 |
| 2 | −6 |
| 3 | −12 |

Proposed answer: y = −x + 1

Step 1: Compute slope using (−1, 12) and (2, −6):
$ m = \frac{-6 - 12}{2 - (-1)} = \frac{-18}{3} = -6 $

But proposed slope is −1 → already mismatch.

Let’s compute full equation:

Using points (−1, 12) and (2, −6):
Slope m = −6
Now find b: use (2, −6):
−6 = −6(2) + b → −6 = −12 + b → b = 6

So equation: y = −6x + 6

Check with (3, −12):
y = −6(3) + 6 = −18 + 6 = −12 ✔

Check with (−1, 12):
y = −6(−1) + 6 = 6 + 6 = 12 ✔

Proposed answer y = −x + 1 gives:
At x = −1: y = 1 + 1 = 2 ≠ 12 ✘
So definitely Incorrect.

Thus:
- Problem 1: Correct
- Problem 2: Correct
- Problem 3: Incorrect

But the image shows all three marked Incorrect — that’s wrong for #1 and #2.

Since the task says: *"Determine if the proposed answer is correct or incorrect"*, we must give the true verdict.

Now, the user only asked to “Solve the problem accurately”, and the format requires a Final Answer.

But what exactly is being asked? Looking at the structure:

- Set C has 3 problems, each with a proposed answer and checkboxes for Correct/Incorrect.
- The instruction: “For each problem below write an equation to represent the table. A proposed answer is given. Determine if the proposed answer is correct or incorrect.”

So the expected output is to label each as Correct or Incorrect.

Thus, final answers per problem:

1. Correct
2. Correct
3. Incorrect

But the format says:
→ Final Answer: [Provide only the final correct answer]

Since there are three items, we should list them clearly.

Let me format as:

Final Answer:
1. Correct
2. Correct
3. Incorrect