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 Slope = -1/5 2

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) 3 4 (-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) 3 4 (-4,3) (-10, 9) -1

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