Graphing linear equations on coordinate planes.

It looks like you've uploaded a set of linear equations (problems 7 through 12), each with a blank coordinate grid for graphing. The task is likely to graph each equation on the provided coordinate plane.

Let's go through each equation one by one, convert it into slope-intercept form ($ y = mx + b $) if needed, find two points, and then explain how to graph it.

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7) $ 2x - y = 3 $

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

- Slope $ m = 2 $
- Y-intercept $ b = -3 $

Find two points:
- When $ x = 0 $: $ y = 2(0) - 3 = -3 $ → point: $ (0, -3) $
- When $ x = 1 $: $ y = 2(1) - 3 = -1 $ → point: $ (1, -1) $

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

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8) $ 2x + 4y = 8 $

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

- Slope $ m = -\frac{1}{2} $
- Y-intercept $ b = 2 $

Find two points:
- When $ x = 0 $: $ y = 2 $ → $ (0, 2) $
- When $ x = 2 $: $ y = -\frac{1}{2}(2) + 2 = -1 + 2 = 1 $ → $ (2, 1) $

Graph: Plot $ (0, 2) $ and $ (2, 1) $, draw a line.

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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 $.

Graph: Draw a vertical line passing through $ x = -6 $ (all points where $ x = -6 $, regardless of $ y $).

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10) $ 3x - 5y = 10 $

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

- Slope $ m = \frac{3}{5} $
- Y-intercept $ b = -2 $

Points:
- $ x = 0 $: $ y = -2 $ → $ (0, -2) $
- $ x = 5 $: $ y = \frac{3}{5}(5) - 2 = 3 - 2 = 1 $ → $ (5, 1) $

Graph: Plot $ (0, -2) $ and $ (5, 1) $, draw a line.

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11) $ 3x + 2y = 7 $

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

- Slope $ m = -\frac{3}{2} $
- Y-intercept $ b = 3.5 $

Points:
- $ x = 0 $: $ y = 3.5 $ → $ (0, 3.5) $
- $ x = 2 $: $ y = -\frac{3}{2}(2) + 3.5 = -3 + 3.5 = 0.5 $ → $ (2, 0.5) $

Graph: Plot $ (0, 3.5) $ and $ (2, 0.5) $, draw a line.

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

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

(Multiply both sides by $-2$ to eliminate fraction)

- Slope $ m = 6 $
- Y-intercept $ b = -4 $

Points:
- $ x = 0 $: $ y = -4 $ → $ (0, -4) $
- $ x = 1 $: $ y = 6(1) - 4 = 2 $ → $ (1, 2) $

Graph: Plot $ (0, -4) $ and $ (1, 2) $, draw a line.

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✔ Summary of Graphing Steps:

For each equation:
1. Rewrite in slope-intercept form $ y = mx + b $ (if possible).
2. Identify the y-intercept.
3. Use the slope to find another point.
4. Plot both points and draw a straight line.

Special case:
- For vertical lines (like #9), just draw a vertical line at the given $ x $-value.

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Since I can't draw on the image, here’s what you should do:

> On each grid:
> - Label axes.
> - Plot the two points we found.
> - Draw a straight line through them.
> - Optionally, label the line with the equation.

Let me know if you'd like me to generate a visual description or help you plot specific points!