linear equations

What is a linear relation?

A linear relation is a relationship between two variables that, when plotted on a graph, forms a straight line. It describes a constant rate of change.

How can a linear relation be represented?

Linear relations can be represented in several ways:

1. Equation: Often in the form y = mx + b
2. Graph: A straight line on a coordinate plane.
3. Table of Values: Shows a constant difference in y-values for a constant difference in x-values.

What is the general form of a linear equation?

The slope-intercept form is y = mx + b, where:

• y and x are variables
• m is the slope of the line
• b is the y-intercept

What does the slope (m) represent in a linear relation?

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates the steepness and direction of the line. It can be calculated as \frac{\text{rise}}{\text{run}} or \frac{\Delta y}{\Delta x}.

What does the y-intercept (b) represent in a linear relation?

The y-intercept (b) is the point where the line crosses the y-axis. It is the value of y when x = 0. It often represents the initial value or starting