Math Problem Statement

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

Solution

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

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

  • (x1,y1)(x_1, y_1) is the first point (1,6)(1, 6)
  • (x2,y2)(x_2, y_2) is the second point (3,2)(-3, 2)

Step 1: Subtract the yy-coordinates

y2y1=26=4y_2 - y_1 = 2 - 6 = -4

Step 2: Subtract the xx-coordinates

x2x1=31=4x_2 - x_1 = -3 - 1 = -4

Step 3: Divide the differences to find the gradient

m=44=1m = \frac{-4}{-4} = 1

Final Answer:

The gradient of the line segment connecting the points (1,6)(1, 6) and (3,2)(-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)(2, 5) and (4,9)(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)(-2, 3) and (1,6)(1, -6)?
  5. How do you find the equation of a line given two points?

Tip: The gradient tells you how much the yy-coordinate changes for each unit change in the xx-coordinate!

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Math Problem Analysis

Mathematical Concepts

Algebra
Analytic Geometry
Slopes of Lines

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 6-8