Linear Relationships

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by the equation y = mx + b, where m is the slope and b is the y-intercept.

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

The slope of a vertical line is undefined because the change in x is zero, which would involve division by zero.

The slope of a horizontal line is 0, indicating that there is no change in the y-value as x changes.

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

'b' represents the y-intercept of the line.

The slope indicates the steepness and direction of the line, while the y-intercept indicates where the line crosses the y-axis.

A slope of 2 means that for every 1 unit increase in x, the value of y increases by 2 units.

A negative slope indicates that as the value of x increases, the value of y decreases, resulting in a downward slant of the line.