Six linear equations graphed with their x-intercepts, y-intercepts, and slopes labeled.

Let's go through each of the given linear equations, analyze the graphs provided (based on the image), and identify the x-intercept, y-intercept, and slope for each line. We’ll also verify if the answers are correct.

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15. y = x - 3

- Graph: A straight line with positive slope.
- x-intercept: Where the line crosses the x-axis (y = 0):
$$
0 = x - 3 \Rightarrow x = 3 \Rightarrow (3, 0)
$$
- y-intercept: Where the line crosses the y-axis (x = 0):
$$
y = 0 - 3 = -3 \Rightarrow (0, -3)
$$
- Slope: From the equation $ y = x - 3 $, the coefficient of $ x $ is 1 → slope = 1

✔ Correct as shown.

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16. 2x + y = 4

Rewriting in slope-intercept form:
$$
y = -2x + 4
$$

- x-intercept: Set $ y = 0 $:
$$
0 = -2x + 4 \Rightarrow 2x = 4 \Rightarrow x = 2 \Rightarrow (2, 0)
$$
- y-intercept: Set $ x = 0 $:
$$
y = -2(0) + 4 = 4 \Rightarrow (0, 4)
$$
- Slope: Coefficient of $ x $ is $-2$ → slope = -2

But in your image, it says y-intercept = (0, -4) — that’s incorrect.

✘ Error: The y-intercept should be (0, 4), not (0, -4).
Also, the graph shows a downward-sloping line from (2, 0) to (0, 4), which matches $ y = -2x + 4 $. So the slope = -2 is correct.

✔ Slope: ✔️
✘ y-intercept: ✘ (should be (0, 4))

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17. y = 3x

- x-intercept: Set $ y = 0 $:
$$
0 = 3x \Rightarrow x = 0 \Rightarrow (0, 0)
$$
- y-intercept: Set $ x = 0 $:
$$
y = 3(0) = 0 \Rightarrow (0, 0)
$$
- Slope: Coefficient of $ x $ is 3 → slope = 3

✔ All correct.

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18. x - 2y = 10

Rewrite in slope-intercept form:
$$
-2y = -x + 10 \Rightarrow y = \frac{1}{2}x - 5
$$

- x-intercept: Set $ y = 0 $:
$$
0 = \frac{1}{2}x - 5 \Rightarrow \frac{1}{2}x = 5 \Rightarrow x = 10 \Rightarrow (10, 0)
$$
- y-intercept: Set $ x = 0 $:
$$
y = \frac{1}{2}(0) - 5 = -5 \Rightarrow (0, -5)
$$
- Slope: $ \frac{1}{2} $

But in your image, it says:
- x-intercept: (2, 0) → ✘ Incorrect
- y-intercept: (0, -5) → ✔ Correct
- slope: 1 → ✘ Incorrect

✘ The x-intercept should be (10, 0), not (2, 0)
✘ Slope should be 1/2, not 1

So this one has two errors.

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19. 6x - 3y = 6

Simplify:
Divide entire equation by 3:
$$
2x - y = 2 \Rightarrow y = 2x - 2
$$

- x-intercept: Set $ y = 0 $:
$$
0 = 2x - 2 \Rightarrow 2x = 2 \Rightarrow x = 1 \Rightarrow (1, 0)
$$
- y-intercept: Set $ x = 0 $:
$$
y = 2(0) - 2 = -2 \Rightarrow (0, -2)
$$
- Slope: 2

In your image:
- x-intercept: (1, 0) → ✔
- y-intercept: (0, 3) → ✘ Should be (0, -2)
- slope: 3 → ✘ Should be 2

✘ y-intercept and slope are incorrect.

---

20. 3x + 2y = 6

Solve for y:
$$
2y = -3x + 6 \Rightarrow y = -\frac{3}{2}x + 3
$$

- x-intercept: Set $ y = 0 $:
$$
0 = -\frac{3}{2}x + 3 \Rightarrow \frac{3}{2}x = 3 \Rightarrow x = 2 \Rightarrow (2, 0)
$$
- y-intercept: Set $ x = 0 $:
$$
y = 3 \Rightarrow (0, 3)
$$
- Slope: $-\frac{3}{2}$

In your image:
- x-intercept: (6, 0) → ✘ Should be (2, 0)
- y-intercept: (0, 3) → ✔
- slope: blank → should be $-\frac{3}{2}$

✘ x-intercept wrong
✘ slope missing

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## ✔ Final Summary:

| Problem | x-intercept | y-intercept | Slope | Correct? |
|--------|-------------|-------------|-------|---------|
| 15 | (3, 0) | (0, -3) | 1 | ✔ |
| 16 | (2, 0) | (0, -4) | -2 | ✘ y-int should be (0, 4) |
| 17 | (0, 0) | (0, 0) | 3 | ✔ |
| 18 | (2, 0) | (0, -5) | 1 | ✘ x-int should be (10, 0), slope = 1/2 |
| 19 | (1, 0) | (0, 3) | 3 | ✘ y-int should be (0, -2), slope = 2 |
| 20 | (6, 0) | (0, 3) | ? | ✘ x-int should be (2, 0), slope = -3/2 |

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## 🔧 Corrections:

16. $ 2x + y = 4 $

- x-intercept: (2, 0) ✔
- y-intercept: (0, 4) ✘ (was written as (0, -4))
- slope: -2 ✔

18. $ x - 2y = 10 $

- x-intercept: (10, 0) ✘ (was (2, 0))
- y-intercept: (0, -5) ✔
- slope: 1/2 ✘ (was 1)

19. $ 6x - 3y = 6 $

- x-intercept: (1, 0) ✔
- y-intercept: (0, -2) ✘ (was (0, 3))
- slope: 2 ✘ (was 3)

20. $ 3x + 2y = 6 $

- x-intercept: (2, 0) ✘ (was (6, 0))
- y-intercept: (0, 3) ✔
- slope: -3/2 ✘ (missing)

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## ✔ Final Answer (Corrected):

| # | Equation | x-intercept | y-intercept | Slope |
|---|----------------|-------------|-------------|---------|
| 15| y = x - 3 | (3, 0) | (0, -3) | 1 |
| 16| 2x + y = 4 | (2, 0) | (0, 4) | -2 |
| 17| y = 3x | (0, 0) | (0, 0) | 3 |
| 18| x - 2y = 10 | (10, 0) | (0, -5) | 1/2 |
| 19| 6x - 3y = 6 | (1, 0) | (0, -2) | 2 |
| 20| 3x + 2y = 6 | (2, 0) | (0, 3) | -3/2 |

> 🟩 Make sure to fix the intercepts and slopes accordingly when filling out the worksheet.

Let me know if you'd like help graphing any of these!