Moving Straight Ahead Math Reflection 1

1. In a linear relationship, the dependent and independent variable go up at a steady rate. For example, say the dependent variable was time (hours) and the independent variable was distance (miles). Bob rode his bike 5 miles in one hour, 10 miles in 2 hours, and 15 miles in 3 hours. This is a steady rate because he is going 5 miles an hour each time. It changes by the same rate. The line on the graph would be straight because the miles are changing by 5 every hour. It has to change by the same rate to actually be a linear relationship.

2. A pattern of change for a linear relationship shows up in a table, graph, and equation of the relationship.

In a table, you can tell if a pattern of change is linear if the numbers are going up at a steady rate. Bob’s table would look like this:

hours|miles
1|5
2|10
3|15
4|20
5|25
6|30
7|35

The independent variable (hours) goes up by 1 as the dependent variable (miles) is going up by 5.

In a graph, if the line is straight, then it is linear because it is changing (or not changing) at the same rate. For every hour, Bob rides his 5 miles an hour, so for every hour on the graph, it would go up by 5 each hour. The line is straight, which shows that it’s linear.

In an equation, if you can find a steady rate, then it’s linear. Bob’s equation would be m=5h (m= total miles, h= number of hours). You know that the rate is 5 miles per hour because 5 is in the equation and it’s a unit rate so you can multiply it by any number to find the total number of miles. And after you find a rate, you know it’s linear.