Slope

In this lesson we will learn about the slope of a line.

The slope of a line is like an incline or a hill. When the line is on the coordinate plane, the numbers tell us how steep it is.

The numbers that describe the slope are written in the form of a ratio or a fraction.

Slope Definition

As you probably remember, this ratio is described as rise over run

A graph showing that the rise is the vertical distance and run is the horizontal distance

Rise describes how much we move up or down from one point to the next. Run describes how much we move left or right from one point to the next.

Go to Explore! Slope to find out more.

Slope Example

Notice in the graph below to get from point A to point B we moved up 3 and right 2.

So the slope of a line between these points is 3 over 2

Graph with point A at (-3, -1) and point B at (-1, 2). It shows the vertical distance 3 and a horizontal distance of 2

slope equals rise over run which equals 3 over 2

Slope Equation

We can also find the slope without to graph the point. This can be done using the slope formula. Notice that the variable (m) is used to represent slope.

Graph with point A at (-3, -1) and point B at (-1, 2).

m equals change in y over change in x, which is (y2 - y1) over (x2 - x1)

Slope Equation Example

Remember from Unit 1 that when working with two points we use special notation to seperate the points. One point we will label (x1, y1) and the other point will be labeled (x2, y2). It does not matter how you label either point. For our example we will label A(-3, -1) as (x1, y1) and B(-1, 2) as (x2, y2). The rest is just placing the values into the correct location of the formula.

Graph with point A at (-3, -1) and point B at (-1, 2). A line is drawn between the 2 points that moves upward from left to right

m equals change in y over change in x, which is (y2 - y1) over (x2 - x1)

See if you can use the given points to find the value of slope.

the slope formula, but with x and y values for each point missing.

Answer: 2 - -1 / -1 - -3

m equals blank over blank

Answer: -3/2

Video example

Slope Video

For a quick interactive view on how to find slope as well as learn information that will help you answer questions on the task assignment visit this site: PH School Slope Video

Slope Practice

Alright, now it is your turn to find slope.

Find the slope of a line that goes through the points C(4, 1) and D(-3, 2). Let C be (x1, y1) and D be (x2, y2).

A graph with points at D (-3, 2) and C (4, 1). The line slopes down from D to C

See if you can use the given points to find the value of slope. Substitute in the appropriate values.

The equation for slope equals (y2 - y1) over (x2 - x1)

The slope equation but with blank x and y values

Answer: 2 - 1 / -3 - 4

m equals blank over blank

Answer: 1/-7

Video example

Slope of a Line

You can tell a lot about the slope by how it slants.

Positive Slope

A line that goes upward as it moves from left to right

Negative Slope

A line that goes downward as it moves from left to right

Undefined Slope

A vertical line

Zero Slope

A horizontal line

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