Worksheet for graphing lines in slope-intercept form with two equations and blank coordinate grids.

Let's solve the problem of graphing lines in slope-intercept form for both equations:

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🔷 Slope-Intercept Form:

The general form is:
$$
y = mx + b
$$
where:
- $ m $ is the slope,
- $ b $ is the y-intercept (the point where the line crosses the y-axis).

We'll use this to graph each line.

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## ✔ Problem 1: $ y = \frac{1}{4}x - 1 $

Step 1: Identify the slope and y-intercept

- Slope $ m = \frac{1}{4} $
- Y-intercept $ b = -1 $ → So, the line passes through the point $ (0, -1) $

Step 2: Plot the y-intercept

Plot the point $ (0, -1) $ on the graph.

Step 3: Use the slope to find another point

Slope = $ \frac{1}{4} $ means:
- Rise = 1 (up 1 unit)
- Run = 4 (right 4 units)

From $ (0, -1) $, move:
- Up 1 → $ y = 0 $
- Right 4 → $ x = 4 $

So, next point is $ (4, 0) $

You can also go down 1 and left 4 to get a point on the other side: $ (-4, -2) $

Step 4: Draw the line

Connect the points $ (0, -1) $ and $ (4, 0) $ with a straight line. Extend it in both directions.

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## ✔ Problem 2: $ y = -x + 2 $

Step 1: Identify the slope and y-intercept

- Slope $ m = -1 $
- Y-intercept $ b = 2 $ → So, the line passes through $ (0, 2) $

Step 2: Plot the y-intercept

Plot the point $ (0, 2) $

Step 3: Use the slope to find another point

Slope = $ -1 $ means:
- Rise = -1 (down 1 unit)
- Run = 1 (right 1 unit)

From $ (0, 2) $, move:
- Down 1 → $ y = 1 $
- Right 1 → $ x = 1 $

So, next point is $ (1, 1) $

Alternatively, go up 1 and left 1: $ (-1, 3) $

Step 4: Draw the line

Connect $ (0, 2) $ and $ (1, 1) $ with a straight line and extend.

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📌 Summary of Graphing Steps:

| Equation | Slope | Y-Intercept | Points to Plot |
|--------|-------|-------------|----------------|
| $ y = \frac{1}{4}x - 1 $ | $ \frac{1}{4} $ | $ (0, -1) $ | $ (0, -1), (4, 0) $ |
| $ y = -x + 2 $ | $ -1 $ | $ (0, 2) $ | $ (0, 2), (1, 1) $ |

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✔ Final Answer:

You should now sketch the following on the grids:

#### For #1:
- Start at $ (0, -1) $
- Go up 1, right 4 → $ (4, 0) $
- Draw a straight line through these points.

#### For #2:
- Start at $ (0, 2) $
- Go down 1, right 1 → $ (1, 1) $
- Draw a straight line through these points.

> The first line rises slowly (positive slope), the second falls steeply (negative slope).

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If you're drawing this by hand:
- Make sure your axes are labeled.
- Mark the points clearly.
- Draw smooth, straight lines.

Let me know if you'd like a visual sketch description or help plotting specific coordinates!