Answer key for a math worksheet on graphing linear equations, showing solutions for eight different lines.

It looks like you've uploaded a worksheet titled "Sketch the Graph of Each Line" with 8 linear equations, and each has a corresponding graph. The image includes a watermark "MATH LAMSA" and an "answer key" label at the top — suggesting this is a solution sheet for graphing linear equations.

However, since the actual image contains graphical representations (lines drawn on coordinate grids), and we can't view images directly in this interface, I'll help you solve and explain how to graph each line based on the given equations.

Let’s go through each equation step-by-step and explain how to sketch its graph. We’ll convert each equation into slope-intercept form:
$$
y = mx + b
$$
where $ m $ is the slope and $ b $ is the y-intercept.

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1) $-7x + 2y = 8$

Solve for $ y $:
$$
2y = 7x + 8 \\
y = \frac{7}{2}x + 4
$$

- Slope ($m$): $ \frac{7}{2} = 3.5 $
- Y-intercept ($b$): $ 4 $

To graph:
- Start at $ (0, 4) $
- Use rise/run: up 7, right 2 → next point: $ (2, 11) $
- Draw line through these points.

✔ This matches a steep upward-sloping line crossing the y-axis at 4.

---

2) $-5x + 2y = 6$

Solve for $ y $:
$$
2y = 5x + 6 \\
y = \frac{5}{2}x + 3
$$

- Slope: $ \frac{5}{2} = 2.5 $
- Y-intercept: $ 3 $

Graph:
- Start at $ (0, 3) $
- Rise 5, run 2 → next point: $ (2, 8) $

✔ Steep positive slope, crosses y-axis at 3.

---

3) $-x + 2y = -8$

Solve for $ y $:
$$
2y = x - 8 \\
y = \frac{1}{2}x - 4
$$

- Slope: $ \frac{1}{2} $
- Y-intercept: $ -4 $

Graph:
- Start at $ (0, -4) $
- Rise 1, run 2 → next point: $ (2, -3) $

✔ Gentle upward slope, crosses y-axis below origin.

---

4) $-3x + 2y = 6$

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

- Slope: $ \frac{3}{2} = 1.5 $
- Y-intercept: $ 3 $

Graph:
- Start at $ (0, 3) $
- Rise 3, run 2 → next point: $ (2, 6) $

✔ Upward slope, crosses y-axis at 3.

---

5) $-5x + 4y = -16$

Solve for $ y $:
$$
4y = 5x - 16 \\
y = \frac{5}{4}x - 4
$$

- Slope: $ \frac{5}{4} = 1.25 $
- Y-intercept: $ -4 $

Graph:
- Start at $ (0, -4) $
- Rise 5, run 4 → next point: $ (4, 1) $

✔ Moderate upward slope, crosses y-axis at -4.

---

6) $-5x + 3y = -9$

Solve for $ y $:
$$
3y = 5x - 9 \\
y = \frac{5}{3}x - 3
$$

- Slope: $ \frac{5}{3} \approx 1.67 $
- Y-intercept: $ -3 $

Graph:
- Start at $ (0, -3) $
- Rise 5, run 3 → next point: $ (3, 2) $

✔ Positive slope, crosses y-axis at -3.

---

7) $x + y = 3$

Solve for $ y $:
$$
y = -x + 3
$$

- Slope: $ -1 $
- Y-intercept: $ 3 $

Graph:
- Start at $ (0, 3) $
- Down 1, right 1 → next point: $ (1, 2) $

✔ Negative slope, diagonal from top-left to bottom-right.

---

8) $7x + 4y = 16$

Solve for $ y $:
$$
4y = -7x + 16 \\
y = -\frac{7}{4}x + 4
$$

- Slope: $ -\frac{7}{4} = -1.75 $
- Y-intercept: $ 4 $

Graph:
- Start at $ (0, 4) $
- Down 7, right 4 → next point: $ (4, -3) $

✔ Steep negative slope, starts at $ (0, 4) $

---

✔ Summary Table:

| Equation | Slope-Intercept Form | Slope | Y-intercept |
|--------|----------------------|-------|-------------|
| 1) $-7x + 2y = 8$ | $ y = \frac{7}{2}x + 4 $ | $ \frac{7}{2} $ | 4 |
| 2) $-5x + 2y = 6$ | $ y = \frac{5}{2}x + 3 $ | $ \frac{5}{2} $ | 3 |
| 3) $-x + 2y = -8$ | $ y = \frac{1}{2}x - 4 $ | $ \frac{1}{2} $ | -4 |
| 4) $-3x + 2y = 6$ | $ y = \frac{3}{2}x + 3 $ | $ \frac{3}{2} $ | 3 |
| 5) $-5x + 4y = -16$ | $ y = \frac{5}{4}x - 4 $ | $ \frac{5}{4} $ | -4 |
| 6) $-5x + 3y = -9$ | $ y = \frac{5}{3}x - 3 $ | $ \frac{5}{3} $ | -3 |
| 7) $x + y = 3$ | $ y = -x + 3 $ | $-1$ | 3 |
| 8) $7x + 4y = 16$ | $ y = -\frac{7}{4}x + 4 $ | $-\frac{7}{4}$ | 4 |

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🔍 How to Check Your Graphs:

1. Find two points:
- Use y-intercept.
- Plug in $ x = 0 $ and $ x = 1 $ or use slope to find another.
2. Plot both points and draw a straight line.
3. Ensure the line passes through the correct intercepts and has the correct direction (up/down).

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📌 Final Notes:

- All graphs should be straight lines.
- Positive slopes go up from left to right; negative slopes go down.
- The answer key likely shows these lines correctly plotted on the grid.

If you’d like, I can generate a text-based representation of each graph using ASCII art or guide you on how to plot them accurately on paper.

Let me know if you'd like me to verify any specific graph or help with plotting steps!