What you’ll learn to do: Find the slope of a line

Visual and verbal cues constantly give us information in our daily lives.  For example, when you wake up in the morning and it is raining, you know that you’ll want to find your umbrella.  Or when you order a vanilla spice latte and see the steam rising, you instinctively start to blow on it before you sip it.  The slope of a line can provide the same kind of cues about what the line represents.

Slope can describe a rapidly increasing trend, something that doesn’t change over time, or a slowly decreasing amount. The beauty of the picture that the slope offers is that once you learn to interpret it, you can do so quickly without long sentences of explanation.

The steepness of the slant of a line is called the slope of the line.   As we’ve been graphing linear equations, we’ve seen that some lines slant up as they go from left to right and some lines slant down. Some lines are very steep and some lines are flatter. What determines whether a line slants up or down, and if its slant is steep or flat?

The concept of slope has many applications in the real world. The pitch of a roof and the grade of a highway or wheelchair ramp are just some examples in which you literally see slopes. And when you ride a bicycle, you feel the slope as you pump uphill or coast downhill.

In this section we will learn how to calculate the slope of a line, and how to interpret what kind of line is represented by different slopes – positive, negative, or zero.

Specifically, in this section you’ll learn how to:

• Find the slope of a line from its graph
• Find the slope of horizontal and vertical lines
• Use the slope formula to find the slope of a line between two points

Before you get started in this module, try a few practice problems and review prior concepts.