Worksheet for writing linear equations in slope-intercept form from given graphs.

Let's solve each graph step by step to find the slope-intercept form of the line:
$$
y = mx + b
$$
where:
- $ m $ is the slope
- $ b $ is the y-intercept

We'll analyze each graph one at a time.

---

🔹 Graph 1 (Top Left)

Step 1: Find the y-intercept (b)
The line crosses the y-axis at $ y = 2 $.
So, y-intercept = 2

Step 2: Find the slope (m)
Pick two points on the line. From the graph:
- At $ x = 0 $, $ y = 2 $
- At $ x = 4 $, $ y = 0 $

Slope $ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2} $

✔ Slope = $-\frac{1}{2}$, y-intercept = 2

Equation:
$$
y = -\frac{1}{2}x + 2
$$

---

🔹 Graph 2 (Top Middle)

Step 1: y-intercept
Line passes through $ (0, 1) $ → y-intercept = 1

Step 2: Slope
From $ (0,1) $ to $ (1,3) $:
$ m = \frac{3 - 1}{1 - 0} = \frac{2}{1} = 2 $

✔ Slope = 2, y-intercept = 1

Equation:
$$
y = 2x + 1
$$

---

🔹 Graph 3 (Top Right)

Step 1: y-intercept
The line crosses the y-axis at $ y = 0 $ → y-intercept = 0

Step 2: Slope
Points: $ (0,0) $ and $ (4,-2) $
$ m = \frac{-2 - 0}{4 - 0} = \frac{-2}{4} = -\frac{1}{2} $

✔ Slope = $-\frac{1}{2}$, y-intercept = 0

Equation:
$$
y = -\frac{1}{2}x
$$

---

🔹 Graph 4 (Bottom Left)

Step 1: y-intercept
Crosses y-axis at $ y = -2 $ → y-intercept = -2

Step 2: Slope
From $ (0,-2) $ to $ (2,2) $:
$ m = \frac{2 - (-2)}{2 - 0} = \frac{4}{2} = 2 $

✔ Slope = 2, y-intercept = -2

Equation:
$$
y = 2x - 2
$$

---

🔹 Graph 5 (Bottom Middle)

Step 1: y-intercept
Crosses y-axis at $ y = 3 $ → y-intercept = 3

Step 2: Slope
From $ (0,3) $ to $ (3,0) $:
$ m = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1 $

✔ Slope = -1, y-intercept = 3

Equation:
$$
y = -x + 3
$$

---

🔹 Graph 6 (Bottom Right)

Step 1: y-intercept
Crosses y-axis at $ y = 1 $ → y-intercept = 1

Step 2: Slope
From $ (0,1) $ to $ (2,3) $:
$ m = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1 $

✔ Slope = 1, y-intercept = 1

Equation:
$$
y = x + 1
$$

---

✔ Final Answers:

#### Graph 1:
- Slope = $-\frac{1}{2}$
- y-intercept = 2
- Equation: $ y = -\frac{1}{2}x + 2 $

#### Graph 2:
- Slope = 2
- y-intercept = 1
- Equation: $ y = 2x + 1 $

#### Graph 3:
- Slope = $-\frac{1}{2}$
- y-intercept = 0
- Equation: $ y = -\frac{1}{2}x $

#### Graph 4:
- Slope = 2
- y-intercept = -2
- Equation: $ y = 2x - 2 $

#### Graph 5:
- Slope = -1
- y-intercept = 3
- Equation: $ y = -x + 3 $

#### Graph 6:
- Slope = 1
- y-intercept = 1
- Equation: $ y = x + 1 $

---

Let me know if you'd like this formatted for printing or want explanations in simpler terms!