Math Problem Statement

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

Solution

To calculate the gradient of a straight line passing through two points, you can use the formula:

Gradient (m)=y2y1x2x1\text{Gradient (m)} = \frac{y_2 - y_1}{x_2 - x_1}

In this case, the two points given are (3,1)(3, 1) and (8,36)(8, 36).

  1. (x1,y1)=(3,1)(x_1, y_1) = (3, 1)
  2. (x2,y2)=(8,36)(x_2, y_2) = (8, 36)

Substitute these values into the formula:

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

Thus, the gradient of the line is 7.

Would you like more details on this, or do you have any further questions?

Here are some related questions for further practice:

  1. What is the gradient of a line passing through the points (4,5)(4, 5) and (7,11)(7, 11)?
  2. How do you calculate the y-intercept of a line if the gradient is known?
  3. Can a gradient be negative? What does a negative gradient indicate about the line?
  4. What is the equation of the line that passes through (3,1)(3, 1) and (8,36)(8, 36)?
  5. How would the gradient change if the two points were closer together?

Tip: The gradient tells you how steep a line is. A larger gradient means the line is steeper!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations

Formulas

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

Theorems

Linear equation gradient

Suitable Grade Level

Grades 7-10