Graphing lines using intercept form worksheet with equations and grids.

Let's solve the problem step by step.

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Task: Graphing Lines Using Intercept Form

We are given 6 linear equations in slope-intercept form:

$$
y = mx + b
$$

Where:
- $ m $ is the slope
- $ b $ is the y-intercept

To graph each line, we can use the y-intercept and the slope to plot two points and draw a straight line through them.

Alternatively, since the question says "using intercept form," let’s clarify:

> The intercept form of a line is:
> $$
> \frac{x}{a} + \frac{y}{b} = 1
> $$
> where $ a $ is the x-intercept and $ b $ is the y-intercept.

But the given equations are in slope-intercept form, so we'll need to convert them into intercept form or use the x- and y-intercepts to graph.

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Step-by-step method for graphing using intercepts:

For each equation:
1. Find the y-intercept: Set $ x = 0 $, solve for $ y $
2. Find the x-intercept: Set $ y = 0 $, solve for $ x $
3. Plot both intercepts on the grid
4. Draw a straight line through them

Let’s do this for each equation.

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1) $ y = 2x - 3 $

- Y-intercept: Let $ x = 0 $
$$
y = 2(0) - 3 = -3 \Rightarrow (0, -3)
$$
- X-intercept: Let $ y = 0 $
$$
0 = 2x - 3 \Rightarrow 2x = 3 \Rightarrow x = \frac{3}{2} = 1.5 \Rightarrow (1.5, 0)
$$

✔ Plot points: $ (0, -3) $ and $ (1.5, 0) $, then draw line.

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2) $ y = -x + 2 $

- Y-intercept: $ x = 0 \Rightarrow y = 2 \Rightarrow (0, 2) $
- X-intercept: $ y = 0 \Rightarrow 0 = -x + 2 \Rightarrow x = 2 \Rightarrow (2, 0) $

✔ Plot $ (0, 2) $ and $ (2, 0) $, draw line.

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3) $ y = 6x - 2 $

- Y-intercept: $ x = 0 \Rightarrow y = -2 \Rightarrow (0, -2) $
- X-intercept: $ y = 0 \Rightarrow 0 = 6x - 2 \Rightarrow 6x = 2 \Rightarrow x = \frac{1}{3} \approx 0.33 \Rightarrow (0.33, 0) $

✔ Plot $ (0, -2) $ and $ (0.33, 0) $, draw line.

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4) $ y = -3x + 1 $

- Y-intercept: $ x = 0 \Rightarrow y = 1 \Rightarrow (0, 1) $
- X-intercept: $ y = 0 \Rightarrow 0 = -3x + 1 \Rightarrow 3x = 1 \Rightarrow x = \frac{1}{3} \approx 0.33 \Rightarrow (0.33, 0) $

✔ Plot $ (0, 1) $ and $ (0.33, 0) $, draw line.

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5) $ y = \frac{2}{3}x $

- Y-intercept: $ x = 0 \Rightarrow y = 0 \Rightarrow (0, 0) $
- X-intercept: $ y = 0 \Rightarrow 0 = \frac{2}{3}x \Rightarrow x = 0 \Rightarrow (0, 0) $

So both intercepts are at the origin.

We need another point. Use slope: rise over run = $ \frac{2}{3} $. From $ (0, 0) $, go up 2, right 3 → $ (3, 2) $

✔ Plot $ (0, 0) $ and $ (3, 2) $, draw line.

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

- Y-intercept: $ x = 0 \Rightarrow y = -2 \Rightarrow (0, -2) $
- X-intercept: $ y = 0 \Rightarrow 0 = -\frac{1}{2}x - 2 \Rightarrow \frac{1}{2}x = -2 \Rightarrow x = -4 \Rightarrow (-4, 0) $

✔ Plot $ (0, -2) $ and $ (-4, 0) $, draw line.

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7) $ y = -x - 1 $

- Y-intercept: $ x = 0 \Rightarrow y = -1 \Rightarrow (0, -1) $
- X-intercept: $ y = 0 \Rightarrow 0 = -x - 1 \Rightarrow x = -1 \Rightarrow (-1, 0) $

✔ Plot $ (0, -1) $ and $ (-1, 0) $, draw line.

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8) $ y = x + 1 $

- Y-intercept: $ x = 0 \Rightarrow y = 1 \Rightarrow (0, 1) $
- X-intercept: $ y = 0 \Rightarrow 0 = x + 1 \Rightarrow x = -1 \Rightarrow (-1, 0) $

✔ Plot $ (0, 1) $ and $ (-1, 0) $, draw line.

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✔ Summary of Intercepts for Each Line:

| Equation | Y-intercept | X-intercept |
|--------|-------------|-------------|
| 1) $ y = 2x - 3 $ | (0, -3) | (1.5, 0) |
| 2) $ y = -x + 2 $ | (0, 2) | (2, 0) |
| 3) $ y = 6x - 2 $ | (0, -2) | (1/3, 0) |
| 4) $ y = -3x + 1 $ | (0, 1) | (1/3, 0) |
| 5) $ y = \frac{2}{3}x $ | (0, 0) | (0, 0) → use (3, 2) |
| 6) $ y = -\frac{1}{2}x - 2 $ | (0, -2) | (-4, 0) |
| 7) $ y = -x - 1 $ | (0, -1) | (-1, 0) |
| 8) $ y = x + 1 $ | (0, 1) | (-1, 0) |

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📌 Instructions for Graphing:

1. On each grid:
- Mark the y-intercept on the vertical axis.
- Mark the x-intercept on the horizontal axis.
- Draw a straight line connecting them.
- Extend the line slightly beyond both points.
- Label the line if needed.

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🔍 Tips:

- For lines passing through origin (like #5), use slope to find a second point.
- Use a ruler to draw straight lines.
- Double-check your calculations.

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✔ Final Answer:

You should now be able to sketch all 8 lines on their respective grids using the intercepts above.

If you'd like, I can generate the actual graphs (as ASCII art or descriptions) for each one. Let me know!