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

Session 5, Part B:

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


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)


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


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


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


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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