Worksheet with four graphs of lines for writing linear equations in slope-intercept form.

Let's solve each of these problems step by step. We are asked to write the slope-intercept form of the equation of each line.

The slope-intercept form is:

$$
y = mx + b
$$

Where:
- $ m $ is the slope of the line,
- $ b $ is the y-intercept (the point where the line crosses the y-axis).

We'll find $ m $ and $ b $ for each graph.

---

1) First Graph

Look at the line on the first grid.

#### Step 1: Find the y-intercept ($b$)
The line crosses the y-axis at $ y = 3 $. So,
$$
b = 3
$$

#### Step 2: Find the slope ($m$)

Use two points on the line. Let's pick:
- $ (-2, 4) $
- $ (0, 3) $

Now calculate the slope:
$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{0 - (-2)} = \frac{-1}{2} = -\frac{1}{2}
$$

So the equation is:
$$
y = -\frac{1}{2}x + 3
$$

✔ Answer for #1: $ \boxed{y = -\frac{1}{2}x + 3} $

---

2) Second Graph

#### Step 1: Find the y-intercept ($b$)

The line crosses the y-axis at $ y = 2 $. So,
$$
b = 2
$$

#### Step 2: Find the slope ($m$)

Pick two points:
- $ (0, 2) $
- $ (2, 0) $

$$
m = \frac{0 - 2}{2 - 0} = \frac{-2}{2} = -1
$$

So the equation is:
$$
y = -x + 2
$$

✔ Answer for #2: $ \boxed{y = -x + 2} $

---

3) Third Graph

#### Step 1: Find the y-intercept ($b$)

The line crosses the y-axis at $ y = -1 $. So,
$$
b = -1
$$

#### Step 2: Find the slope ($m$)

Pick two points:
- $ (0, -1) $
- $ (1, 2) $

$$
m = \frac{2 - (-1)}{1 - 0} = \frac{3}{1} = 3
$$

So the equation is:
$$
y = 3x - 1
$$

✔ Answer for #3: $ \boxed{y = 3x - 1} $

---

4) Fourth Graph

#### Step 1: Find the y-intercept ($b$)

The line crosses the y-axis at $ y = -2 $. So,
$$
b = -2
$$

#### Step 2: Find the slope ($m$)

Pick two points:
- $ (0, -2) $
- $ (1, 1) $

$$
m = \frac{1 - (-2)}{1 - 0} = \frac{3}{1} = 3
$$

So the equation is:
$$
y = 3x - 2
$$

✔ Answer for #4: $ \boxed{y = 3x - 2} $

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✔ Final Answers:

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

Let me know if you'd like a visual explanation or help with any other problems!