what does a linear relationship tell you 
there are three sets of necessary criteria an equation has to meet in order to qualify as a linear one an equation expressing a linear relationship can t consist of more than two variables all of the variables in an equation must be to the first power and the equation must graph as a straight line a commonly used linear relationship is a correlation which describes how close to linear fashion one variable changes as related to changes in another variable in econometrics linear regression is an often used method of generating linear relationships to explain various phenomena it is commonly used in extrapolating events from the past to make forecasts for the future not all relationships are linear however some data describe relationships that are curved such as polynomial relationships while still other data cannot be parameterized linear functionsmathematically similar to a linear relationship is the concept of a linear function in one variable a linear function can be written as follows f x m x b where m slope b y intercept begin aligned f x mx b textbf where m text slope b text y intercept end aligned f x mx bwhere m slopeb y intercept this is identical to the given formula for a linear relationship except that the symbol f x is used in place of y this substitution is made to highlight the meaning that x is mapped to f x whereas the use of y simply indicates that x and y are two quantities related by a and b in the study of linear algebra the properties of linear functions are extensively studied and made rigorous given a scalar c and two vectors a and b from rn the most general definition of a linear function states that c f a b c f a c f b c times f a b c times f a c times f b c f a b c f a c f b examples of linear relationshipslinear relationships are pretty common in daily life let s take the concept of speed for instance the formula we use to calculate speed is as follows the rate of speed is the distance traveled over time if someone in a minivan is traveling between sacramento and marysville in california a 44 1 mile stretch on highway 99 and the complete journey ends up taking about 45 minutes they will have been traveling just below 60 mph while there are more than two variables in this equation it s still a linear equation because one of the variables will always be a constant distance a linear relationship can also be found in the equation distance rate x time because distance is a positive number in most cases this linear relationship would be expressed on the top right quadrant of a graph with an x and y axis if a bicycle made for two was traveling at a rate of 30 miles per hour for 20 hours the rider would end up traveling 600 miles represented graphically with the distance on the y axis and time on the x axis a line tracking the distance over those 20 hours would travel straight out from the convergence of the x and y axis in order to convert celsius to fahrenheit or fahrenheit to celsius you would use the equations below these equations express a linear relationship on a graph c 5 9 f 3 2 degree c frac 5 9 degree f 32 c 95 f 32 f 9 5 c 3 2 degree f frac 9 5 degree c 32 f 59 c 32 assume that the independent variable is the size of a house as measured by square footage which determines the market price of a home the dependent variable when it is multiplied by the slope coefficient of 207 65 and is then added to the constant term 10 500 if a home s square footage is 1 250 then the market value of the home is 1 250 x 207 65 10 500 270 062 50 graphically and mathematically it appears as follows in this example as the size of the house increases the market value of the house increases linearly some linear relationships between two objects can be called a proportional relationship this relationship appears asy k x where k constant y x proportional quantities begin aligned y k times x textbf where k text constant y x text proportional quantities end aligned y k xwhere k constanty x proportional quantities 