What is the gradient of the line segment connecting the points (1,6) and (-3,2)?

To find the **gradient (slope)** of the line segment connecting two points, we use the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Where:
- \( (x_1, y_1) \) is the first point \( (1, 6) \)
- \( (x_2, y_2) \) is the second point \( (-3, 2) \)

### Step 1: Subtract the \( y \)-coordinates
\[
y_2 - y_1 = 2 - 6 = -4
\]

### Step 2: Subtract the \( x \)-coordinates
\[
x_2 - x_1 = -3 - 1 = -4
\]

### Step 3: Divide the differences to find the gradient
\[
m = \frac{-4}{-4} = 1
\]

### Final Answer:
The gradient of the line segment connecting the points \( (1, 6) \) and \( (-3, 2) \) is **1**.

Would you like more details or further explanation?

Here are 5 related questions for practice:

1. What is the gradient of the line connecting \( (2, 5) \) and \( (4, 9) \)?
2. How do you interpret a gradient of 0?
3. What is the gradient of a vertical line?
4. Can you find the gradient between the points \( (-2, 3) \) and \( (1, -6) \)?
5. How do you find the equation of a line given two points?

**Tip:** The gradient tells you how much the \( y \)-coordinate changes for each unit change in the \( x \)-coordinate!

Learn how to calculate the gradient of a line segment connecting two points (1,6) and (-3,2) using the slope formula. This step-by-step guide explains the method clearly, making it suitable for students in Grades 6-8.

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