We will now look at the rate of change, m, on a graph.

Introduction to Slope, m

The graph of a linear function is a straight line.

So, we can say

So, we can say

𝑦 1

𝒙𝟐𝒙𝟏

Pt. 1

Pt. 2

𝑦 2

We can show the locations of the x and y parts of the points on the graph as below:

Find the slope, m, of the linear function:

𝑦 1

𝒙𝟐𝒙𝟏

Pt. 1

Pt. 2 𝑦 2

Change in y

𝒎=𝒄𝒉𝒂𝒏𝒈𝒆𝒊𝒏 𝒚𝒄𝒉𝒂𝒏𝒈𝒆𝒊𝒏𝒙

is 3.

is the vertical count up (or down which is a negative number) from point to point.is the count

is the horizontal count right (or left which is a negative number) from point to point.is the countChange in

x is 4.

We say when x changes by 4, there is a change in y of 3 from point to point.

𝒎=𝟑𝟒

Find the slope, m, of the linear function:

𝑦 1

𝒙𝟐𝒙𝟏𝑦 2

Pt. 1Pt. 2 Change in

y

𝒎=𝒄𝒉𝒂𝒏𝒈𝒆𝒊𝒏 𝒚𝒄𝒉𝒂𝒏𝒈𝒆𝒊𝒏𝒙

is 1.

is the vertical count up (or down which is a negative number) from point to point.is the count

is the horizontal count right (or left which is a negative number) from point to point.is the count

Change in x

is 2.

We say when x changes by 1, there is a change in y of 2 from point to point.

𝒎=𝟏𝟐

Using the slope, m, can you find another point on the graph?

Pt. 3 Change in y

𝒎=𝟏𝟐

is the vertical count up so we count up 1 from known point, then:

is the horizontal count right so we count right 2 .

Change in x

2

1

This is the location of the new point, pt. 3.

Write the new point as an ordered pair:

Find the slope of the linear function, then locate one more point. Write the ordered pair for this point.

Pt. 3

-2

is the vertical count down.

is the horizontal count right so we count right 3 .3

Using the slope as a repeating pattern, we locate a new point.

The new point written as an ordered pair is

is -2.

is 3.

𝒎=−𝟐𝟑

Find the slope of the linear function, then locate one more point. Write the ordered pair for this point.

Pt. 3

-2

is also called the rise.

is the run .3

is -2.

is 3.

The slope,m, also the rate of change, for this linear function is: