- Why is the x-coordinate in ordered pairs always first?
Many things in mathematics and in everyday life are done by agreement so that we will all understand one another. If we didn't have an agreement for the order of the x- and y-coordinates in ordered pairs, some people would read them with the x first and others would read them with the y first. This would cause confusion about how to graph the point. We agree to do other things in math as well. For example, we agree that the x-coordinates to the right of the y-axis are positive and the x-coordinates to the left of the y-axis are negative. In everyday life, we agree to drive on the right side of the road in the United States. However, in Australia they agree to drive on the left side of the road. Knowing these agreements can be very helpful!
- Why should I bother learning this?
The ability to locate points on the coordinate plane was one of the major mathematics achievements of the twentieth century. Coordinate geometry linked algebra and geometry together and opened the doors to many other achievements in both mathematics and science, such as the study of calculus. Your students will need to be able to graph relationships as they proceed through school. Coordinate graphs are commonly used by newspapers, television, medical research, and the business world to show relationships between two variables, such as the production levels versus costs in a business, exposure to tobacco smoke versus cancer rates, amount of money earned versus education level, student-to-teacher ratio versus the quality of education, and the height of a person versus age. Have your students look for graphs which show relationships in newspapers and magazines.
- Are all graphs of equations going to be straight lines?
Have students examine the equation x2 = y. Have them make a table of values for x and y and then graph them. They will see that the graph is not a straight line. Tell them that many of the equations they will study when they are older are not linear equations. Stress that the equations they will study this year are linear and will help them understand future equations in the years ahead.
Graphing Linear Equations