Graphing linear equations on coordinate planes.

Since I can't view or access images directly, I’ll help you solve each of the linear equations listed and explain how to graph them on the coordinate plane. You can then plot the lines on the provided grids.

We'll go through each equation one by one, rewrite it in slope-intercept form (if needed), find two points, and describe how to graph it.

---

7) $ 2x - y = 3 $

Step 1: Solve for $ y $:
$$
2x - y = 3 \Rightarrow -y = -2x + 3 \Rightarrow y = 2x - 3
$$

- Slope: 2
- Y-intercept: $ (0, -3) $

Find another point:
Let $ x = 1 $:
$ y = 2(1) - 3 = -1 $ → Point: $ (1, -1) $

Graphing:
Plot $ (0, -3) $ and $ (1, -1) $, draw a line through them.

---

8) $ 2x + 4y = 8 $

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

- Slope: $ -\frac{1}{2} $
- Y-intercept: $ (0, 2) $

Another point:
Let $ x = 2 $:
$ y = -\frac{1}{2}(2) + 2 = -1 + 2 = 1 $ → Point: $ (2, 1) $

Graphing:
Plot $ (0, 2) $ and $ (2, 1) $, draw the line.

---

9) $ x + 1 = -5 $

This is not in terms of $ y $. Let's simplify:
$$
x + 1 = -5 \Rightarrow x = -6
$$

This is a vertical line at $ x = -6 $.

Graphing:
Draw a vertical line passing through $ x = -6 $, regardless of $ y $. It goes straight up and down through all points where $ x = -6 $, e.g., $ (-6, 0), (-6, 1), (-6, -1) $, etc.

---

10) $ 3x - 5y = 10 $

Step 1: Solve for $ y $:
$$
3x - 5y = 10 \Rightarrow -5y = -3x + 10 \Rightarrow y = \frac{3}{5}x - 2
$$

- Slope: $ \frac{3}{5} $
- Y-intercept: $ (0, -2) $

Another point:
Let $ x = 5 $:
$ y = \frac{3}{5}(5) - 2 = 3 - 2 = 1 $ → Point: $ (5, 1) $

Graphing:
Plot $ (0, -2) $ and $ (5, 1) $, draw the line.

---

11) $ 3x + 2y = 7 $

Step 1: Solve for $ y $:
$$
3x + 2y = 7 \Rightarrow 2y = -3x + 7 \Rightarrow y = -\frac{3}{2}x + \frac{7}{2}
$$

- Slope: $ -\frac{3}{2} $
- Y-intercept: $ (0, 3.5) $

Another point:
Let $ x = 1 $:
$ y = -\frac{3}{2}(1) + 3.5 = -1.5 + 3.5 = 2 $ → Point: $ (1, 2) $

Graphing:
Plot $ (0, 3.5) $ and $ (1, 2) $, draw the line.

---

12) $ 3x - \frac{1}{2}y = 2 $

Step 1: Solve for $ y $:
$$
3x - \frac{1}{2}y = 2 \Rightarrow -\frac{1}{2}y = -3x + 2 \Rightarrow y = 6x - 4
$$

Multiply both sides by $ -2 $:
$$
y = 6x - 4
$$

- Slope: 6
- Y-intercept: $ (0, -4) $

Another point:
Let $ x = 1 $:
$ y = 6(1) - 4 = 2 $ → Point: $ (1, 2) $

Graphing:
Plot $ (0, -4) $ and $ (1, 2) $, draw the line.

---

✔ Summary of Graphing Steps:

For each equation:
1. Rewrite in slope-intercept form $ y = mx + b $ (except vertical lines).
2. Plot the y-intercept.
3. Use the slope to find a second point.
4. Draw a straight line through the points.

---

Final Notes:

- For vertical lines like #9 ($ x = -6 $), just draw a vertical line at that $ x $-value.
- Make sure to use the grid carefully—each square typically represents 1 unit.
- Label your axes if needed.

If you'd like, I can provide a table of points for each equation or guide you step-by-step for plotting on the grid. Just let me know!