Linear Relationships Prep

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 constant of proportionality is the constant value (k) that relates two proportional quantities. In the equation y = kx, k represents the constant of proportionality.

To find the constant of proportionality, divide the dependent variable (y) by the independent variable (x) for any pair of values. For example, if 14 gallons of gas cost $48.86, the constant of proportionality is $48.86 / 14.

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 unit change in x.

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

A relationship is proportional if the ratio of the dependent variable to the independent variable is constant. This means that the graph of the relationship will pass through the origin (0,0).

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The slope of the line y = 3x + 4 is 3.

A nonproportional relationship means that the ratio of the dependent variable to the independent variable is not constant. The graph will not pass through the origin.

To extend a linear relationship in a table, use the equation of the line to calculate the dependent variable (y) for new values of the independent variable (x).