Question
A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go, and it steadily rose 3 feet per second.
Write an equation that shows the relationship between the number of seconds since the boy let the balloon go, x, and its elevation in feet, y.
y=
Write an equation that shows the relationship between the number of seconds since the boy let the balloon go, x, and its elevation in feet, y.
y=
Answers
GPT-4o mini
To write the equation that shows the relationship between the number of seconds since the boy let the balloon go (denoted as \( x \)) and its elevation in feet (denoted as \( y \)), we start with the initial height of the balloon and the rate at which it rises.
The balloon starts at an elevation of 3 feet (when \( x = 0 \)), and it rises at a rate of 3 feet per second. Therefore, for every second that passes, you can express the elevation as:
\[ y = \text{initial height} + \text{(rate of rise)} \times \text{(time in seconds)} \]
Putting the values in:
- Initial height = 3 feet
- Rate of rise = 3 feet/second
The equation can be expressed as:
\[ y = 3 + 3x \]
where:
- \( y \) is the elevation in feet,
- \( x \) is the number of seconds since the balloon was let go.
So, the final equation is:
\[ y = 3 + 3x \]
The balloon starts at an elevation of 3 feet (when \( x = 0 \)), and it rises at a rate of 3 feet per second. Therefore, for every second that passes, you can express the elevation as:
\[ y = \text{initial height} + \text{(rate of rise)} \times \text{(time in seconds)} \]
Putting the values in:
- Initial height = 3 feet
- Rate of rise = 3 feet/second
The equation can be expressed as:
\[ y = 3 + 3x \]
where:
- \( y \) is the elevation in feet,
- \( x \) is the number of seconds since the balloon was let go.
So, the final equation is:
\[ y = 3 + 3x \]