Jack measured the height of tree he planted and wrote an equation to describe its growth. The equation he wrote is: y = 6x + 10. Which of the following statements would be true?
6 is the initial height
10 is the rate the tree is growing
The equation y = 6x + 10 describes the growth of the tree planted by Jack.
Here are some statements that would be true based on the equation:
1. The initial height of the tree (when x = 0) is 10 units.
2. For every 1 unit increase in x (time or number of days), the height of the tree increases by 6 units.
3. The rate of growth of the tree is constant and equal to 6 units per unit of time.
4. The height of the tree is directly proportional to the time passed, with a constant rate of change of 6 units per unit of time.
5. If the tree is 3 years old (x = 3), its height is 6 * 3 + 10 = 28 units.
Note: These statements are based solely on the equation and may not reflect real-world conditions accurately.
To determine which of the given statements would be true, we need to analyze the equation y = 6x + 10. This is a linear equation where y represents the height of the tree and x represents the time in years or any other unit of measurement.
1. The tree began at a height of 6 feet: This statement is not necessarily true. The equation y = 6x + 10 represents the growth of the tree, not its initial height. The constant term (+10) indicates that the tree already had a height of 10 units (e.g., feet) before it started growing.
2. The tree grows at a constant rate: This statement is true. In the equation y = 6x + 10, the coefficient of x is 6, indicating that for every unit of time (x), the tree grows by 6 units in height (y).
3. The tree will eventually reach a height of 100 feet: This statement cannot be determined solely from the given equation. To find out if the tree will reach a height of 100 feet, we would need to determine the value of x that corresponds to a height of 100 feet. Setting y = 100 in the equation and solving for x would give us the answer.
4. The tree will never stop growing: This statement is not true based on the given equation. According to y = 6x + 10, the growth of the tree is determined by the variable x, which represents time. If x stops increasing, the growth of the tree will also stop.
In summary, the only true statement based on the given equation is: "The tree grows at a constant rate."