Question

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

Answer 1

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.

Answer 2

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.