1.) Describe how the dependent variable changes as the independent variable changes in a linear relationship. Give examples.
In a linear relationship, the dependent variable changes at a constant rate as the independent variable changes. For example, If a person bikes 8 miles per hour, than in 2 hours they would have rode 16 miles. The hours are the independent variable, and the miles are the dependant variable. In this example, the dependant variable goes at a constant rate of 8 miles for every hour. This constant rate would continue and there would be 16 miles for 2 hours, then 24 miles for 3 hours, then 32 hours for 4 hours, and so on.

2.) How does the pattern of change for a linear relationship show up in a table, a graph, and an equation of the relationship?

The pattern of change for a linear relationship shows up in a table because you can see the constant rate and how the numbers change. For example, if there is a table where x went 2,3,4,5 and the y went 20, 30, 40, 50, than this would be a linear relationship. This would be a linear relationship because there is a constant rate. The constant rate for x is +1 and the constant rate for y is +10.

The pattern of change for a linear relationship, shows up in a graph, because the data points on the graph create a straight line. The graph above is a linear relationship because the rate is constant and the line is straight. For the graph above, the constant rate is, for every time that the hours increase by 1, the miles increase by 50.
For the example, look at the top of the page.

The pattern of change for a linear relationship shows up in an equation because the equation is linear as long as there are no exponents. The number in the equation shows the amount of change of the dependant variable.

For example:
t=hours d=miles

7t=d
This equation means that they are going 7 miles per hour. The 7 is the unit rate of how far they go in one hour. Since there are no exponents, the equation is a linear relationship. Also, the 7 tells you the amount of change. If the number in the equation was 8 than the person would be going faster, at 8 miles per hour.