Math Problem Statement

The equation of a line is y = 11x + 8. What is the gradient of the line?

Solution

The equation provided is in the slope-intercept form y=mx+cy = mx + c, where:

  • mm represents the gradient (or slope) of the line.
  • cc represents the y-intercept.

In the equation y=11x+8y = 11x + 8, the coefficient of xx is 11. Therefore, the gradient of the line is:

Gradient=11\text{Gradient} = 11

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

  1. How would the graph of the line change if the gradient were negative?
  2. What is the y-intercept of the line, and how is it interpreted?
  3. How can you find the equation of a line given two points on it?
  4. How would you determine the gradient of a line parallel to this one?
  5. How would you find the x-intercept of the line given the equation?

Tip: In linear equations, the gradient tells you how steep the line is. A larger gradient means a steeper slope.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-Intercept Form: y = mx + c

Theorems

Properties of Linear Equations
Slope and Gradient Theorem

Suitable Grade Level

Grades 8-10