In order to have a good understanding of the forthcoming topic on Business Algebra, it is imperative to have a good grasp and understanding of previous topics before. The most significant is the graphical representation and interpretation of a given set of data. This is because graphical interpretation of data is widely common in business algebra and it cannot be avoided. Hence, if there are and difficulties in the plotting of a data set, and in its interpretation, then the understanding and utilization of the product output would be futile. It is therefore important to have a good knowledge of this area.
Linear equations provide information on how quickly data is rising or falling, and this is known as the slope or gradient of the equation. The gradient is usually a quotient of the values on the x-axis and the y-axis, with the x-axis values as the numerators. The slope of the graph is a representation of the change in values of the given data set. Linear equations are usually in the form of y= mx+ c, where y represents values on the vertical axis of a graph and x the values on the horizontal axis, m is the gradient or slope of the graph and it can be positive or negative whereas c represents the point where the lie graph intersects the y-axis.
A real life application of the linear equation would be in the population demographics of a country in population census analysis. The population of a country may be analyzed for the many times that a census has been carried out. In this case, the population, say in millions of people, would lie on the y-axis while the years would be on the x-axis. By plotting the population value of a given census interval for the number of census done, a linear graph would be obtained. This would not pass through the origin and a linear equation in the form of y= mx+ c would be obtained. In this equation, the y-value would represent the population number at a given time (year) represented by x-value. Therefore, the population of a country at any given year can be predicted. The slope of the graph, m, would in this case give the rate at which the population is increasing with time, and it can be used to project the expected population of a country in the future, assuming that all other constants are maintained. This may then help the government for example on budgetary allocations. A positive slope would represent an increase while a negative slope shows that there is a decrease in the population.