Each day, a young person should sleep 7 hours plus 1/4 hour for each year that the person is under 18 years of age. Assuming the relation is linear, write the equation relating hours of sleep y and age x.
y = 7 + (1/4)(18-x) for x <= 18
y = 7 for x > 18
y=7 9/2+ 1/4 x
To write the equation relating hours of sleep y and age x, let's break down the given information step-by-step:
1. Each day, a young person should sleep 7 hours.
2. Additionally, for each year that the person is under 18 years of age, they should sleep an extra 1/4 hour.
Now, let's denote y as the hours of sleep and x as the age of the person.
According to step 1, the base hours of sleep is 7.
According to step 2, for each year that the person is under 18, they should sleep an extra 1/4 hour. Since the relation is linear, we can express this using the equation:
Extra hours = (1/4) * (18 - x)
We subtract x from 18 because it represents how many years the person is under 18.
Finally, we can combine the base hours and extra hours to get the total hours of sleep y:
y = 7 + (1/4) * (18 - x)
Therefore, the equation relating hours of sleep y and age x is y = 7 + (1/4) * (18 - x).
To write the equation relating hours of sleep (y) and age (x), we need to find the equation of a linear relation that satisfies the given conditions.
We know that a young person should sleep 7 hours plus 1/4 hour for each year that the person is under 18 years of age. This means that when the person is 0 years old, they should sleep 7 + 1/4(0) = 7 hours. When the person is 18 years old, they should sleep 7 + 1/4(18) = 11.5 hours.
Let's assume the equation of the linear relation is:
y = mx + b
where 'm' represents the rate of change (slope) and 'b' represents the y-intercept.
To find the slope (m), we can use the difference in sleep hours (y) for two different ages (x) divided by the difference in ages:
m = (change in y) / (change in x)
Using the points (0, 7) and (18, 11.5), we can calculate the slope:
m = (11.5 - 7) / (18 - 0) = 4.5 / 18 = 1/4
So, the slope of the linear relation is 1/4, which indicates that for each year, the sleep hours increase by 1/4 hour.
Now, let's find the y-intercept (b) by substituting one of the given points into the equation:
7 = (1/4)(0) + b
7 = 0 + b
b = 7
Therefore, the equation relating hours of sleep (y) and age (x) is:
y = (1/4)x + 7