This lesson explores the relationship between x and y values in equations by examining graph shapes. It begins with a review of graphing linear equations, highlighting common misconceptions about graph shapes. The lesson then presents two examples: Sheila's running pace, illustrating direct variation with a straight line, and Angie's sandbox dimensions, demonstrating inverse variation with a curved line. The lesson concludes by comparing these graph types, emphasizing the differences in proportionality and rate of change.

What is a common misunderstanding about graphing equations?

• All equations result in a straight line.

• All equations result in a curved line.

• Equations cannot be graphed.

• Equations always have the same shape.

In Sheila's running example, what does the graph represent?

• A constant relationship with no change.

• An inverse variation with a curved line.

• A direct variation with a straight line.

• A non-proportional relationship.

What is the unit rate in Sheila's running example?

• 15 minutes per mile

• 10 minutes per mile

• 20 minutes per mile

• 5 minutes per mile

In Angie's sandbox example, what happens as the width increases?

• The area decreases.

• The area increases.

• The length decreases.

• The length increases.

What type of graph is formed in Angie's sandbox example?

• A horizontal line graph.

• A curved line graph.

• A vertical line graph.

• A straight line graph.

How do the variables change in an inverse variation?

• They remain constant.

• Both increase at a constant rate.

• Both decrease at a constant rate.

• One increases while the other decreases.

What is the main difference between direct and inverse variations?

• Direct variations have straight lines, inverse have curved lines.

• Both have curved lines.

• Direct variations have curved lines, inverse have straight lines.

• Both have straight lines.