TODAY’S LESSON: TODAY’S LESSON: SLOPE SLOPE

(i.e. tilt, lean, pitch, tip …)(i.e. tilt, lean, pitch, tip …)

More Slope

-3

-2

-1

0

1

2

3

4

5

0 1 2 3

Linear Equations x-y notation functional notation describe lines: y = mx + b f(x) = mx + b

Every linehas “SLOPE”

Less Slope

-3

-2

-1

0

1

2

3

4

5

0 1 2 3

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:

run

rise

x

y

xx

yy

lengthchange

heightchangeSLOPE

12

12

_

_

Height 3”

4” length

%7575.0"4

"3SLOPE

*Note: Roads have warnings for 8% slope

Using triangles, measure and calculate the slope of one of thesides 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 equationsfor 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 we’ve learned about slope to determine the heel height of a15º 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.

LengthLength LengthLength

ShoeShoe

SlopeSlope

lengthlength

HeelHeel

HeightHeight

33 8”8” 6”6” ??

66 9”9” 6.75”6.75” ??

99 10”10” 7.5”7.5” ??

1212 11”11” 8.3”8.3” ??

What is the formula to find the heel height?

Slope = (change height)/(change length)

15º (Slope given) = (heel height)/lengthtan 15º = .27 (using trig function we willlearn later in the year). Find the heelheights.

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.

LengthLength LengthLength

ShoeShoe

SlopeSlope

lengthlength

HeelHeel

HeightHeight

33 8”8” 6”6” 1.62”1.62”

66 9”9” 6.75”6.75” 1.8”1.8”

99 10”10” 7.5”7.5” 2.1”2.1”

1212 11”11” 8.3”8.3” 2.24”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”