TODAY’S LESSON: SLOPE (i. e. tilt, lean, pitch, tip …) Linear Equations describe lines: x-y notation y = mx + b functional notation 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 = 3 x – 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? Answer: 2) A line with infinite slope? y = 4 or y = -1 or similar horizontal lines. 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 we’ve 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. Length Slope Heel What is the formula to find the heel height? Shoe length Height Slope = (change height)/(change length) 3 8” 6” ? 15º (Slope given) = (heel height)/length 6 9” 6. 75” ? tan 15º =. 27 (using trig function we will 9 10” 7. 5” ? learn later in the year). Find the heel heights. 12 11” 8. 3” ?

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. Length Slope Shoe length Heel Height 3 8” 6” 1. 62” 6 9” 6. 75” 1. 8” 9 10” 7. 5” 2. 1” 12 11” 8. 3” 2. 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”