According to a study conducted in the U.S, a woman's optimal weight is 100 pounds when her height is 5 feet and 130 pounds when her height is 5.5 feet.
- Write a linear equation for a woman's optimal weight in pounds based on the number of inches of her height.
- What does the equation give as the optimal weight of a woman who is 6 feet tall?
- Write a linear equation for a woman's optimal weight in pounds based on the number of inches of her height.
- What does the equation give as the optimal weight of a woman who is 6 feet tall?
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h₁ = 5
w₁ = 100
h₂ = 5.5
w₂ = 130
m = (y₂ - y₁) / (x₂ - x₁)
Subbing known values,
m = (130 - 100) / (5.5 - 5)
m = 30 / 0.5
m = 60
b = w₁ - m(h₁)
Subbing,
b = 100 - 60(5)
b = 100 - 300
b = - 200
Weight-to-Height Function:
w(h) = 60h - 200
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When h = 6 ft.,
w(6) = 60(6) - 200
w(6) = 360 - 200
w(6) = 160
A 6-ft. tall woman's optimum
weight would be 160 lbs.
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w₁ = 100
h₂ = 5.5
w₂ = 130
m = (y₂ - y₁) / (x₂ - x₁)
Subbing known values,
m = (130 - 100) / (5.5 - 5)
m = 30 / 0.5
m = 60
b = w₁ - m(h₁)
Subbing,
b = 100 - 60(5)
b = 100 - 300
b = - 200
Weight-to-Height Function:
w(h) = 60h - 200
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
When h = 6 ft.,
w(6) = 60(6) - 200
w(6) = 360 - 200
w(6) = 160
A 6-ft. tall woman's optimum
weight would be 160 lbs.
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Converting everything into inches because part of the problem says "based on the nubmer of inches of her height"
f(60) = 100
f(66) = 130
Slope = rise/run = 30/6 = 5
Point slope formula = y - 130 = 5(x - 66)
Simplifying gets you y = 5x - 200
For woman who is 6 feet (72 inches)
y = 5x - 200
y = 5(72) - 200
y = 160
f(60) = 100
f(66) = 130
Slope = rise/run = 30/6 = 5
Point slope formula = y - 130 = 5(x - 66)
Simplifying gets you y = 5x - 200
For woman who is 6 feet (72 inches)
y = 5x - 200
y = 5(72) - 200
y = 160