According to the center of Science in the Public Interest, the maximum healthy weight for a person who is 5 feet, 5 inches is 150 pounds and the maximum healthy weight for a person 6 feet, 3 inches tall is 200 pounds. The relationship between weight and height is linear.
When I saw the word LINEAR, I immediately thought about y = mx + b.
Find an equation that gives the maximum healthy weight y for a person whose height is x inches over 4 feet, 10 inches.
HINTS GIVEN IN MATH BOOK:
x = 0 represents a person 4 feet, 10 inches
x = 2 represents a person 5 feet tall, etc.
The correct equation is y = 5x + 115. I was able to find the slope 5 and got as far as y = 5x. My question is: where did 115 come from?
I look forward to your insight and guidance.
Thanks
5 ft, 5 inches = 5.4166667 feet
6 ft, 3 inches = 6.25 feet
so I look at the given data as 2 ordered pairs,
(5.4166667 , 150) and (6.25 , 200)
slope = (200-150)/(6.25-5.4166667) = 60
so y = 60x + b
using the point (6.25,200)
so a person 4 ft 10 inches tall or 4.8333333 ft should weigh
y = 4.8333333(60) - 175 = 115 lbs
I really do not understand their hint.
200 = 60(6.25) + b
b = -175
so my equation is
y = 60x - 175 , where x is feet and y is lbs.
checking the other point
if x = 5.4166667
y = 60(5.4166667) - 175 = 150
my equation works for both data values.
Thank you. I also played with this question some more and learned that
y = 5x - 175 works just the same. You said the slope is 60 but 60 inches divided by 12 inches = 5 feet. I decided to use 5 for the slope.
Both equations work very well.
To find the equation that gives the maximum healthy weight y based on a person's height x inches over 4 feet, 10 inches, you need to use the information provided by the Center of Science in the Public Interest (CSPI) and the hints given in the math book.
According to the CSPI, the maximum healthy weight for a person who is 5 feet, 5 inches (or 65 inches) tall is 150 pounds. And the maximum healthy weight for a person who is 6 feet, 3 inches (or 75 inches) tall is 200 pounds.
From the hints in the math book, we know that for every additional inch in height starting from 4 feet, 10 inches (or 58 inches), the height increases by 1 and the weight increases by 5 pounds, indicating a linear relationship.
Now let's break down the problem step by step:
1. Calculate the height in inches above 4 feet, 10 inches:
x = height - 58
2. Determine the slope (m) based on the given information:
slope = (200 - 150) / (75 - 65) = 5
3. Use the point-slope form of a linear equation, y - y1 = m(x - x1), with the point (65, 150) - representing a person who is 5 feet, 5 inches (or 65 inches) tall and weighs 150 pounds:
y - 150 = 5(x - 65)
4. Simplify the equation:
y - 150 = 5x - 325
5. Move the constant term to the other side:
y = 5x - 325 + 150
6. Combine the constant terms:
y = 5x - 175
However, this equation is calculated relative to the starting point of 4 feet, 10 inches. To align it with the starting point of 0, we need to adjust it.
7. Notice that when x = 0 (a person with a height of 4 feet, 10 inches), y should be 0 (a healthy weight of 0 pounds, as it is not possible to have negative weight):
0 = 5(0) + b
Solve for the y-intercept (b):
0 = b
Therefore, b = 0.
8. Substitute the value of b = 0 into the equation:
y = 5x + 0
Simplifying further, we get the equation:
y = 5x
So, the equation that gives the maximum healthy weight y for a person whose height is x inches over 4 feet, 10 inches is y = 5x.
I apologize, there was an error in my previous response where I mentioned the constant term as 115. It should have been 0, as explained above. Thank you for bringing it to my attention.