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**Objective The student will be able to:**

Determine the slope of a line between 2 points, on a graph, and in an equation. Compare the slopes of two different lines.

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Career Focus Mathematics is used by architects to express the design images on a drawing that can then be used by construction workers to build that image for everyone to see. Mathematics is needed to analyze and calculate structural problems in order to engineer a solution that will assure that a structure will remain standing and stable. The sizes and shapes of the elements of a design are possible to describe because of mathematical principles such as slope, linear lines, area, and perimeter.

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**Activating Strategy What is the meaning of this sign?**

Icy Road Ahead Steep Road Ahead Curvy Road Ahead Trucks Entering Highway Ahead

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**Slope is the steepness of a line.**

What does the 7% mean? 7% 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. 7 feet 100 feet Give the students an example of a road with 7 percent steepness: Plaza Rd. is a road that is on a hill and is 300 ft. long. The top of the road is 21 ft. higher than the bottom of the road. As you drive in your car 100 ft. up Plaza Rd., you are 7 feet higher above the ground. So, what is slope??? Slope is the steepness of a line.

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**Slope can be expressed different ways:**

A line has a positive slope if it is going uphill from left to right. These are also listed on your Slope Foldable from our previous unit. Positive slope: as “x” increases, “y” increases Negative slope: as “x” increases, “y” decreases A line has a negative slope if it is going downhill from left to right.

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**Slope Intercept Form Y =MX + B**

Ex.) Slope can be easily identified as “m” Y = 4x + 2 Y = 1/5x + 5 Y = 2x + 5 Remind students of slope intercept form and that this is the easiest way to identify slope. Call on students to identify the “m”

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**1) Determine the slope of the line.**

Remind them that: Rise = direction up or down (+/-) Run = left or right (+/-) When given the graph, it is easier to apply “rise over run”.

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**Determine the slope of the line.**

Start with the lower point and count how much you rise and run to get to the other point! rise 3 = = run 6 6 Also point out that 3/6 and ½ are equivalent to each other and represent the SAME SLOPE. Ask students to come up with an equivalent fraction and demonstrate how the slope would still lead to points on the line. 3 Notice the slope is positive AND the line increases!

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**2) Find the slope of the line that passes through the points (-2, -2) and (4, 1).**

When given points, it is easier to use the formula! y2 is the y coordinate of the 2nd ordered pair (y2 = 1) y1 is the y coordinate of the 1st ordered pair (y1 = -2)

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**You can do the problems either way! Which one do you think is easiest?**

Did you notice that Example #1 and Example #2 were the same problem written differently? 6 3 (-2, -2) and (4, 1) Ask students how it can be possible for a graph and an equation to represent the same information Reinforce idea of equivalency You can do the problems either way! Which one do you think is easiest?

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**AP #1: Find the slope of the line that passes through (3, 5) and (-1, 4).**

-4 - ¼

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**Find the slope of the line that goes through the points (-5, 3) and (2, 1).**

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**Determine the slope of the line shown.**

-2 -½ 2

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**Determine the slope of the line.**

-1 Find points on the graph. Use two of them and apply rise over run. 2 The line is decreasing (slope is negative).

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**What is the slope of a horizontal line?**

The line doesn’t rise! All horizontal lines have a slope of 0.

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**What is the slope of a vertical line?**

The line doesn’t run! All vertical lines have an undefined slope.

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**Remember the word “VUXHOY”**

Vertical lines Undefined slope X = number; This is the equation of the line. Horizontal lines O - zero is the slope Y = number; This is the equation of the line. X = 5, y = 4

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**Comparing the slopes of 2 lines**

Sometimes, you will have to compare the slopes of two lines, and they may be in different forms. Ex.) an equation and a graph The greater slope will be the steeper line

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**Comparing the slopes of 2 lines**

Which line is steeper? The graph or the equation? Y = (1/4)X+ 2 1 3

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**AP #2: Which line is steeper?**

Graph: Line between 2 points: (–2, –7) and (3, 8) Allow students to complete Assessment Prompt #2 (3 questions) Graph: Slope of +1 Points: Slope of +3

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**AP #2: Which line is steeper?**

Line Z that passes through points (-1, -8) and (4, 7) or Line J that passes through (2, 3) and (5, 9).

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Which line is steeper? Look at the following 2 graphs. Explain your answer in 1 complete sentence. Since graph #2 is a horizontal line, it has a slope of zero, which automatically makes graph #1 steeper

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Real-Life Scenario Franklin is an architect. He wants to build a house so his elderly grandpa can easily travel up and down the stairs. The following equation and points represent two possible slopes for the staircase. Which one should Franklin choose to build and explain why. Y = 5x (3, 5) (4, 7)

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**Now, I can… Determine the slope of an equation**

Determine the slope of a graph between 2 points Compare 2 different slopes Determine which slope is the steepest Identify horizontal and vertical lines Reason how to use slope in a real world scenario

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