Math Problem Statement

What is the gradient of the straight line that passes through the points (3, 1) and (8, 36)?

Solution

The problem asks for the gradient (slope) of the straight line passing through the points (3,1)(3, 1) and (8,36)(8, 36).

The formula to calculate the gradient mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

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

Substituting the given points:

m=36183=355=7m = \frac{36 - 1}{8 - 3} = \frac{35}{5} = 7

So, the gradient of the line is 77.

Would you like more details or have any questions?

Here are some related questions for further practice:

  1. How would the gradient change if one of the points had different coordinates?
  2. Can you find the equation of the line passing through (3,1)(3, 1) and (8,36)(8, 36)?
  3. What is the significance of the gradient in real-world problems?
  4. How do you calculate the gradient if the line is vertical or horizontal?
  5. What happens to the gradient if the x-coordinates are swapped?

Tip: The steeper the line, the greater the gradient's absolute value. If the line goes downwards, the gradient will be negative!

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slopes of Lines

Formulas

m = (y2 - y1) / (x2 - x1)

Theorems

Gradient formula

Suitable Grade Level

Grades 7-9