Day in and day out, people add and subtract. If you have a pie to share, you try to make sure it is equally divided. When you are running late for an appointment, you mentally calculate the distance and the speed at which the traffic is moving to get an estimate of how late you will be. You also use linear equations, an integral part of arithmetic, during your daily routine.
Linear equations contain one or two variables. The word "linear" comes from the fact that the graph of the equation is a straight line. For example: x+y=10 is a linear equation with two variables--x and y. A variable, as opposed to a constant, can take on different values, depending on the equation.
Linear Equations in Everyday Life
People tend not to think in terms of equations and formulas in their daily lives. They use language to describe the situation. But words can be translated into the language of mathematics. Take a very simple example: A mother has to divide six apples among three children. Effortlessly she reaches the conclusion that each child gets two apples. What she has used is the mathematical function of division to reach the answer: 6/3=2.
Calculating Travel Times
Suppose your office is 30 miles away from home. You have to get there at 8 a.m., and know that the traffic is moving at 60 miles per hour. To find out the time you should leave home, translate the word problem into an equation: time taken = distance divided by the rate of travel. So t (time) = d (distance)/r (rate), and t=30/60. So t=1/2 or half an hour. To reach the office at 8 a.m., you should leave at 7:30 a.m.
Converting Hours to Minutes
How many minutes are there in four hours? Let x = the number of hours, and y = the number of minutes. By definition, there are 60 minutes in one hour. So you can write a linear equation to describe this relationship: y = 60x. The number of minutes equals 60 times the number of hours. For example, let x = 4. Then plug the number into the linear equation to get y = 60*4. So y = 240 minutes.
Weights and Measures
Say your recipe calls for 100 grams of flour, but you can only weigh in ounces. You use a mathematical formula to convert grams to ounces. Or you measure the driveway to figure out how much concrete you will need to pave it. Budgeting, investing, sewing, cooking--math is everywhere.