Representations of Linear Relationships

Draw

Create a graph that shows three lines with slopes $$\frac15$$ , $$\frac35$$ , and $$\frac65$$ . Use the provided grid to draw the lines.

Multiple Choice

The graph shows the height in inches, $$h$$ , of a bamboo plant $$t$$ months after it has been planted. Which equation describes the relationship between $$h$$ and $$t$$ ?

• h = 4t + 5
• h = 2t
• h = 3t
• h = 5t - 10

Open Ended

The graph shows the height in inches, $$h$$ , of a bamboo plant $$t$$ months after it has been planted. How tall will the bamboo plant be after 18 months? Explain or show your reasoning.

Open Ended

A group of hikers park their car at a trail head and walk into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, $$d$$ , from the car after $$h$$ hours of hiking. 1. How far is the campsite from their car? Explain how you know.

Multiple Choice

A group of hikers park their car at a trail head and walk into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, $$d$$ , from the car after $$h$$ hours of hiking.

What is the equation that describes the relationship between $$d$$ and $$h$$ ?

• d = 2h + 5
• d = h + 5
• d = 3h + 2
• d = 4h - 1

Multiple Choice

A group of hikers park their car at a trail head and walk into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, $$d$$ , from the car after $$h$$ hours of hiking.

What is the equation that describes the relationship between $$d$$ and $$h$$ ?

• d = 2h + 5
• d = h + 5
• d = 3h + 2
• d = 4h - 1

Multiple Choice

A group of hikers park their car at a trail head and walk into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, $$d$$ , from the car after $$h$$ hours of hiking.

What is the equation that describes the relationship between $$d$$ and $$h$$ ?

• d = 2h + 5
• d = h + 5
• d = 3h + 2
• d = 4h - 1

Open Ended

A group of hikers park their car at a trail head and walk into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, $$d$$ , from the car after $$h$$ hours of hiking. 3. After how many hours of hiking will they be 16 miles from their car? Explain or show your reasoning.

Multiple Choice

A publisher wants to figure out how thick their new book will be. The book has a front cover and a back cover, each of which have a thickness of $$\frac{1}{4}$$ of an inch. Bond paper has a thickness of $$\frac{1}{4}$$ inch per one hundred pages. Write an equation for the total thickness of the book in inches, $$y$$ , if it has $$x$$ hundred pages, printed on bond paper.

• y = rac{1}{4} + rac{1}{2}x
• y = rac{1}{2} + rac{1}{8}x
• y = rac{1}{4} + rac{1}{4}x
• y = \frac{1}{2} + \frac{1}{4}x

Multiple Choice

A publisher wants to figure out how thick their new book will be. The book has a front cover and a back cover, each of which have a thickness of $$\frac{1}{4}$$ of an inch. Ledger paper has a thickness of $$\frac{2}{5}$$ inch per one hundred pages. What is the equation for the total thickness of the book in inches, $$y$$ , if it has $$x$$ hundred pages, printed on ledger paper?

• y = rac{1}{2} + rac{3}{5}x
• y = rac{1}{4} + rac{1}{5}x
• y = \frac{1}{2} + \frac{2}{5}x
• y = rac{1}{2} + rac{1}{4}x

Multiple Choice

A publisher wants to figure out how thick their new book will be. If they instead chose front and back covers of thickness $$\frac{1}{3}$$ of an inch, how would this change the equations for bond paper and ledger paper?

• The new total thickness will be T + \frac{2}{3} inches.
• The new total thickness will be T + 1 inch.
• The new total thickness will be T + rac{1}{3} inches.
• The new total thickness will be T + rac{1}{2} inches.

Multiple Choice

What is the equation of the line shown in the graph?

• y = x + 1
• y = -x + 3
• y = 2x - 1
• y = 3x + 2