MSA Math Reflection 1

MSA Math Reflection 1

1.In a linear relationship, both the independent and dependent variables change. Particularly in a linear relationship the dependent variable increases at a steady rate as the independent variable increases. For example, if the two variables are miles and hours, the miles would be the dependent variable. In a graph if the number of hours increased by 1 and the number of miles traveled for one hour are 5, then the rate would be 5 miles per hour. Let’s say Catlin rode for 6 hours, on a graph, for every one of those 6 hours the distance would increase by 5. Therefore the relationship is increasing at a steady rate and that is what makes the relationship linear. This is how the dependent and independent variables change in a linear relationship.

2.The pattern of change in a linear relationship can show up in a graph, table and equation. In a graph the linear relationship is represented by a straight line, whether it is increasing or decreasing. For example, Jack rides his bike 6 miles for every hour. That means that the rate of change would be 6. This is because for every hour the graph will increase by 6. If he rides for 5 hours, he rides a total of 30 miles. In a graph, Jack’s rate would show up as a straight line or linear relationship. A linear relationship can also show up in a table. This is shown when the dependent variable in a table increases at a steady rate. For example,

Jack’s biking rate- 6 miles per hour

Hours -1 2 3 4 5

Miles - 6 12 18 24 30

Jack’s rate increases at a steady rate therefore the linear relationship is expressed thought this table. The rate of change is also expressed through this table because you can see that for every hour the distance is increasing by 6.

Lastly a linear relationship is expressed through an equation. This is because if the equation includes the unit rate it is a linear relationship. For example,

Jack’s equation D=distance T=time d= 6t

The unit rate is 6 and therefore the equation is a linear relationship. This is because the unit rate can be multiplied by any number of hours and get the distance that Jack traveled for that number of hours.If this equation was shown on a graph the line would be straight and increasing at a steady rate. The rate of change is represented through his equation because since the unit rate is 6, the distance would increase by6 for whatever number of hours. This is why 6 is the rate of change.