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 expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

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

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

The independent variable is the variable that is manipulated or changed, while the dependent variable is the variable that is measured or affected in response to changes in the independent variable.

A linear relationship can be identified if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

The equation is typically in the form y = initial amount + rate of change * x.

This is represented as c = flat fee + (variable cost per mile * m), where c is the total cost and m is the number of miles.

A proportional relationship is a specific type of linear relationship that passes through the origin (0,0) and can be expressed as y = kx, where k is a constant.

To graph a linear equation, you can plot the y-intercept on the y-axis and use the slope to find another point. Then, draw a straight line through the points.