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Slope and y-intercept Lesson 8-3 p.397

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**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

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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?

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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.

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**Slope and y-intercept Let’s try another one.**

What is the y-intercept of this graph?

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**Slope and y-intercept Let’s try another one.**

What is the y-intercept of this graph? Yes, it is -3.

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**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.

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Slope This is a positive slope This is a negative slope.

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**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.

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**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)

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**Example Notice the two yellow points on the**

Line. Each one is identified as a Whole number ordered pair.

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**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.

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**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.

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**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”

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Try This Name the slope of each line.

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Try This Name the slope of each line. Slope = Slope = -1/5 2

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**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

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**Slope Consider the ordered pairs (3,2) and (7,5)**

The first ordered pair has the x1 and y1 The next one has the x2 and y2 Substitute the numbers into the formula And then solve: y2 – y1 = slope x2 – x1 5 – 2 = 3 7 –

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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)

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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) (-10, 9)

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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) (-10, 9) -1

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Agenda PA# 14 Pp #1,3, odd

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**Please have out HW, red pen, and book.**

2-5-10 Please have out HW, red pen, and book. Start correcting HW

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Agenda PA# 15 Workbook p.67 #1-10

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