More Linear Relationships

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Look For Patterns in a Growing Situation.

Look for a growing pattern. Describe the pattern you see.

(1). If your pattern continues growing in the same way, how many tiles of each color will be in the 4th diagram?

(2). The 5th diagram?

(3). The 10th diagram?

(4). How many tiles of each color will be in theth diagram? 

(5). Explain your reasoning.

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Use a Graph of Linear Relationships to Answer Questions.

Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she’ll read over the next few days.

(1). Find the point where the line crosses the vertical axis. What does that point tell you about the situation?

After day 1, Lin reaches page 70, which matches the point (1, 70) she made on her graph. After day 4, Lin reaches page 190, which does not match the point  (4, 160) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.

(2). Sketch a line showing Lin’s original plan on the axes.

(3). What does the vertical intercept mean in this situation? 

(4). How do the vertical intercepts of the two lines compare?

(5). What does the slope mean in this situation? 

(6). How do the slopes of the two lines compare?

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Draw the Graph of a Linear Relationship by First Creating a Table of Values.

First, complete the table of values. Then graph the linear relation by dragging points onto the number plane to match the table of values.

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Explain what the slope and intercept mean in the following situation.

A graph represents the perimeter, ,  in units, for an equilateral triangle with side length   units. The slope of the line is 3 and the -intercept is 0.

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Customers at the gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the situation.

(1). What does the slope of the line shown by the points mean in this situation?

(2). What does the vertical intercept mean in this situation?

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Jada’s grandparents started a savings account for her in 2010. The table shows the amount in the account each year.

(1). If this relationship is graphed with the year on the horizontal axis and the amount in dollars on the vertical axis, what is the vertical intercept?

(2). What does it mean in this context?