Math Problem Statement

the gradient of y=3x-4

Solution

The gradient of the line given by the equation y=3x4y = 3x - 4 is the coefficient of xx. In this linear equation, the standard form is y=mx+cy = mx + c, where mm represents the gradient (or slope) and cc represents the y-intercept.

Here, m=3m = 3. Therefore, the gradient of the line is:

Gradient=3\text{Gradient} = 3

Would you like more details or have any other questions?

Here are 5 related questions you might find useful:

  1. What is the significance of the y-intercept in the equation y=3x4y = 3x - 4?
  2. How do you determine the gradient from two points on a line?
  3. What is the interpretation of a negative gradient?
  4. How do you find the equation of a line parallel to y=3x4y = 3x - 4?
  5. How do you find the equation of a line perpendicular to y=3x4y = 3x - 4?

Tip: The gradient of a line determines how steep the line is; a higher gradient means a steeper slope.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Gradient/Slope

Formulas

y = mx + c

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-9