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Learning Math Home
Patterns, Functions, and Algebra
 
Session 5 Part A Part B Part C Part D Part E Homework
 
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Session 5 Materials:
Notes
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Session 5, Part B:
Slope

In This Part: Thinking About Slope | Comparing Slopes | Slopes and Architecture

Slope is an important concept in mathematics, and in Part B we'll explore how it is used to solve problems. Note 5

Problem B1

Solution  

Take a minute to think about what you already know about slope. What does it mean? Where is it used?


 
 

You may be familiar with the idea of slope as a measure of steepness. The formula for slope is usually described as:

slope = (change in y) / (change in x)

slope

The slope of a line is often described as a ratio of rise/run. Another way to think of slope is as the amount that the dependent variable changes for each increase by 1 in the independent variable. In other words, as x changes by 1, what happens to y?

Look at these four graphs. For each graph, select four pairs of points, and calculate the slope of the line between each pair of points. Remember that slope = (change in y) / (change in x). As you calculate the slopes for each of the graphs, ask yourself why the slope between pairs of points would change or why it would stay the same. Note 6


 
 

 

Problem B2

Solution  

What happened when you tried to find the ratio of rise/run for the fourth example, a curved object?


 
 

The drawing below shows a cable attached to a wall.

curve and wall


 

Problem B3

Solution  

Calculate the ratio rise/run for each pair of points:
Note 7

 

Points P and Q

 

Points P and R

 

Points Q and R


 

Problem B4

Solution  

Describe the difference between the rise/run ratios for the graph in Problem B3 and the ratios for the graph of a line.
Note 8


Next > Part B (Continued): Comparing Slopes

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