Download Slopes and y-intercept

Slope and y-intercept
Lesson 8-3 p.397
Slope and y-intercepts

When studying lines and their graphs (linear
equations), we can notice two things about
each graph.

Slope—is the steepness of a line.
y-intercept—is the point where the line
crosses the y-axis

Slope and y-intercept

Let’s start with the y-intercept. That is the
easiest to identify:
Notice the graph at the left. What
is the point on the y-axis where the
graph of the line crosses the y-axis?
Slope and y-intercept

Let’s start with the y-intercept. That is the
easiest to identify:
Notice the graph at the left. What
is the point on the y-axis where the
graph of the line crosses the y-axis?
Yes, it crosses the y-axis at “2” We
would say that the y-intercept is 2.
Slope and y-intercept

Let’s try another one.
What is the y-intercept of this graph?
Slope and y-intercept

Let’s try another one.
What is the y-intercept of this graph?
Yes, it is -3.
Slope

Let’s look at some basic characteristics of
slope.

If a line goes uphill from left to right, we say
the slope is positive.

If the line goes downhill from left to right, we
say the slope is negative.
Slope
This is a positive slope.
This is a negative slope.
Slope
There are a couple of unusual situations. The graph on the left
Has a slope of zero.
This one is called undefined.
Copy this down for now. . .the reason will be explained later.
Slope
Now let’s take a look at how to calculate slope.
Write this down: slope = rise
run
To identify the slope of a line, we simply count
lines up or down, (that is the rise) and count
lines across (that is the run). Then we write our
answer as a fraction. (ratio)

Rise is vertical change (UP is positive, DOWN is negative)
Run is horizontal change (RIGHT is positive , LEFT is negative)
Example
Notice the two yellow points on the
Line. Each one is identified as a
Whole number ordered pair.
Example
Notice the two yellow points on the
Line. Each one is identified as a
Whole number ordered pair.
Starting from the lower point, we
Rise 2 lines until we are even with
The next point.
Example
Notice the two yellow points on the
Line. Each one is identified as a
Whole number ordered pair.
Starting from the lower point, we
Rise 2 lines until we are even with
The next point.
Then we run 1 to reach the second
Point. The rise = 2 and the run = 1.
Example
Notice the two yellow points on the
Line. Each one is identified as a
Whole number ordered pair.
Starting from the lower point, we
Rise 2 lines until we are even with
The next point.
Then we run 1 to reach the second
Point. The rise = 2 and the run = 1.
In this case the slope or rise = 2
run
1
Or simply “2”
Try This

Name the slope of each line.
Try This

Name the slope of each line.
Slope = 3
2
Slope = -1/5
Slope




There is another way to find the slope.
In the previous example we found the slope
by counting lines on the coordinate plane.
If no picture is given, but instead 2 ordered
pairs are given we can calculate the slope.
Copy this down: y2 – y1 = slope
x2 – x1
Slope
Consider the ordered pairs (3,2) and (7,5)
The first ordered pair has the x1 and y1
3
2
The next one has the x2 and y2
7
5
Substitute the numbers into the formula
And then solve:
y2 – y1 = slope
x2 – x1
5–2=3
7–3 4
Try This

Using the slope formula, find the slope of the
line that crosses through these points:

(8, -1) (0, -7)

(-4,3)
(-10, 9)
Try This

Using the slope formula, find the slope of the
line that crosses through these points:

(8, -1) (0, -7)

(-4,3)
(-10, 9)
3
4
Try This

Using the slope formula, find the slope of the
line that crosses through these points:

(8, -1) (0, -7)
3
4

(-4,3)
-1
(-10, 9)
2-4-11 Agenda
PA#
14
Pp.400-401
#1,3,5 11-21 odd
2-5-10
 Please
have out HW,
red pen, and book.
 Start correcting HW
2-8-10 Agenda
PA#
15
 Workbook
p.67 #1-10