# TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line.

## Presentation on theme: "TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line."— Presentation transcript:

TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line has SLOPE What things can you think of that have slope, besides lines? Roads, roof of house, ski slope, plumbing in home.

Using triangles, identify a side of the triangle that has: 1) Less SLOPE 2) More SLOPE 3) Zero SLOPE 4) Infinite SLOPE Definition of slope: Height 3 4 length *Note: Roads have warnings for 8% slope

Using triangles, measure and calculate the slope of one of the sides of the triangle. Graph the following sloped lines on graph paper: 1)Slope = 2 2) slope = -2 3) slope = 6 *Hint: pick a point on the graph and use rise over run. Using x-y notation for linear equations (i.e. y = 3x – 2), write linear equations for the following lines: 1) A line with zero slope? 2) A line with infinite slope? Answer: 1) A line with zero slope? y = 4 or y = -1 or similar horizontal lines. Answer: 2) A line with infinite slope? x = 1 or x = -4 or similar vertical lines.

In a letter to European Urology, Dr. Maria Cerruto indicated that women who wore high heel shoes with a 15º slope to the ground developed stronger pelvic muscles. Use what weve learned about slope to determine the heel height of a 15º sloped high heel shoe. Here is a table showing a few shoe sizes along with the shoe length. Since the slope of a shoe is measured from about the ball of your foot to the heel, the length for slope is reduced by 1/4 of the total length.LengthLengthShoeSlopelengthHeelHeight386? 696.75? 9107.5? 12118.3? What is the formula to find the heel height? Slope = (change height)/(change length) 15º (Slope given) = (heel height)/length tan 15º =.27 (using trig function we will learn later in the year). Find the heel heights.

Even though the letter to European Urology by Dr. Maria Cerruto indicated benefits from wearing high heels, there are many other studies that indicate high heel shoes cause hammertoes, bunions, corns, calluses, distorted Achilles muscle, and even schizophrenia. Regular exercise and good diet produce the most benefits.LengthLengthShoeSlopelengthHeelHeight3861.62 696.751.8 9107.52.1 12118.32.24 tan 15º (Slope given) = 0.27 = (heel height)/length = heel height/6 Heel height = 0.27 x 6 = 1.62 Heel height = 0.27 x 6.75 = 1.8 Heel height = 0.27 x 7.5 = 2.1 Heel height = 0.27 x 8.3 = 2.24

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The text passage is a lesson on the concept of slope in linear equations, including definitions, examples, and exercises. It also contains a real-world application of slope in the context of high heel shoes and their effects on pelvic muscles.
multiple_questions_with_answers

the passage contains multiple questions and exercises related to the concept of slope, and answers are provided for some of these questions. specifically, the passage includes:
- questions about identifying sides of a triangle with different slopes.
- exercises to graph lines with given slopes.
- questions to write linear equations for lines with zero and infinite slopes, with answers provided.
- a real-world application problem involving the calculation of heel heights for high heel shoes, with answers provided.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line.

## Presentation on theme: "TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line."— Presentation transcript:

TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line has SLOPE What things can you think of that have slope, besides lines? Roads, roof of house, ski slope, plumbing in home.

Using triangles, identify a side of the triangle that has: 1) Less SLOPE 2) More SLOPE 3) Zero SLOPE 4) Infinite SLOPE Definition of slope: Height 3 4 length *Note: Roads have warnings for 8% slope

Using triangles, measure and calculate the slope of one of the sides of the triangle. Graph the following sloped lines on graph paper: 1)Slope = 2 2) slope = -2 3) slope = 6 *Hint: pick a point on the graph and use rise over run. Using x-y notation for linear equations (i.e. y = 3x – 2), write linear equations for the following lines: 1) A line with zero slope? 2) A line with infinite slope? Answer: 1) A line with zero slope? y = 4 or y = -1 or similar horizontal lines. Answer: 2) A line with infinite slope? x = 1 or x = -4 or similar vertical lines.

In a letter to European Urology, Dr. Maria Cerruto indicated that women who wore high heel shoes with a 15º slope to the ground developed stronger pelvic muscles. Use what weve learned about slope to determine the heel height of a 15º sloped high heel shoe. Here is a table showing a few shoe sizes along with the shoe length. Since the slope of a shoe is measured from about the ball of your foot to the heel, the length for slope is reduced by 1/4 of the total length.LengthLengthShoeSlopelengthHeelHeight386? 696.75? 9107.5? 12118.3? What is the formula to find the heel height? Slope = (change height)/(change length) 15º (Slope given) = (heel height)/length tan 15º =.27 (using trig function we will learn later in the year). Find the heel heights.

Even though the letter to European Urology by Dr. Maria Cerruto indicated benefits from wearing high heels, there are many other studies that indicate high heel shoes cause hammertoes, bunions, corns, calluses, distorted Achilles muscle, and even schizophrenia. Regular exercise and good diet produce the most benefits.LengthLengthShoeSlopelengthHeelHeight3861.62 696.751.8 9107.52.1 12118.32.24 tan 15º (Slope given) = 0.27 = (heel height)/length = heel height/6 Heel height = 0.27 x 6 = 1.62 Heel height = 0.27 x 6.75 = 1.8 Heel height = 0.27 x 7.5 = 2.1 Heel height = 0.27 x 8.3 = 2.24

Download ppt "TODAYS LESSON: SLOPE (i.e. tilt, lean, pitch, tip …) Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b Every line."

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user
The text passage is a lesson on the concept of slope in linear equations, including definitions, examples, and exercises. It also contains a real-world application of slope in the context of high heel shoes and their effects on pelvic muscles.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS

The passage contains multiple questions and exercises related to the concept of slope, and answers are provided for some of these questions. Specifically, the passage includes:
- Questions about identifying sides of a triangle with different slopes.
- Exercises to graph lines with given slopes.
- Questions to write linear equations for lines with zero and infinite slopes, with answers provided.
- A real-world application problem involving the calculation of heel heights for high heel shoes, with answers provided.