Math Reflection 1


1. The dependent variable changes as the independent variable changes in a linear relationship. Usually, the independent variable and the dependent variable will go up or down at a steady rate, or, the dependent variable will not change no matter how much the independent variable changes. In some math problems, you will find that the independent variable changes and the dependent variable will not change, or stay the same. In other math problems, you will find that the independent variable will change by 1, or some other number, and the dependent variable will change by the same number each time, either up or down. For example: a biker rides 3 miles per hour. In 2 hours, she rides 6 miles, in 3 hours; she rides 9 miles, and so on. Each time she rides 1 more hour (hours; independent variable), she goes 3 more miles (miles; dependent variable). Another example is: Marlena is walking in a walkathon. She walks 1.5 meters in 1 second; she walks 3 meters in 2 seconds; she walks 4.5 meters in 3 seconds, and so on. Each time she walks 1 more second, she goes 1.5 more meters. This is why the dependent variable changes as the independent variable changes in a linear relationship.

2. The pattern change for a linear relationship shows up in a table, a graph, and an equation.

The pattern of change for a linear relationship shows up in a graph by showing a straight line. The straight line could be horizontal, diagonal going towards the sky, or diagonal going towards the ground. In a graph, this straight line would be caused by the rate of change. For example: Suzie was doing a walkathon for her school. She recorded her data in a coordinate graph. She walked 2.5 meters per second. So, some of her coordinate pairs are: (1, 2.5), standing for 2.5 meters per second, (2, 5), standing for 5 meters per 2 seconds, (3, 7.5), standing for 7.5 meters per 3 seconds, and (4, 10), standing for 10 meters per 4 second. The line on her graph would look like a diagonal line going tawards the sky.




The pattern of change for a linear relationship shows up in a table by the numbers rising or falling at a constant rate. For example: Nina is walking in a walkathon. Her constant rate is 1.3 meters per second. If she goes at a constant rate of 1.3 meters per second, she will go 2.6 meters per 2 seconds, 3.9 meters per 3 seconds, and so on. First, she goes 1.3 meters per second. Then, she goes another second, so she goes 2.6 meters per 2 seconds. From 1 to 2, she goes 1 more second. From 1.3 to 2.6, she goes 1.3 more meters, and so on. If you continue the pattern, she would go at a constant rate of 1.3 meters per 1 second.



The pattern of change for a linear relationship shows up in an equation because the equation contains the unit rate. For example: Nina’s equation would be:

m=number of meters s=number of seconds

m=1.3s

The unit rate shows a steady rate. Because the steady rate is multiplied by the number of seconds, it will tell you the number of meters. You can multiply any number by the unit rate, and have it be linear on a graph, though, you may need a very large graph!