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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. We can show the locations of the x and y parts of the points on the graph as below:. Pt. 2. So, we can say. Pt. 1. So, we can say. - PowerPoint PPT Presentation
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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: