The table shows the relationship between the height of a tomato plant and the number of days since it has been planted.
Days: 2,5,8,12,18,22,25,30,32,35
Height: 3,4,6,9,13,15,16,20,21,24
What does the y-intercept represent in this problem situation? Explain your answer.
I'm stuck, please help me understand!
The dependent variable goes on the Y axis and the Independent variable goes on the X axis. You can't control time so it goes on the X axis. In this case days goes on the X axis and the height goes on the Y. The Y-intercept would be the point where the line intercepts the Y axis, as you probably know. Hope that helps. It also might help to draw the table out on a graph.
In this example the table starts on day 2 with a height of 3. The Y-intercept is 3, because that is where it starts and crosses the Y axis...😃
If x is the number of days, then the y-intercept is the plant's original height (day 0). I guess no measurements were taken until the 2nd day.
In the given problem situation, the y-intercept represents the initial height of the tomato plant when it was first planted. It is the value of the dependent variable (height) when the independent variable (days) is zero. In this case, when the plant was first planted (at day 0), the height was not provided in the table. So, we do not have the exact value of the y-intercept from the given data. However, by looking at the provided values, we can assume that the y-intercept is zero, meaning the plant initially had no height when it was planted.
To understand the meaning of the y-intercept in this problem situation, let's first understand what the y-intercept represents in general. In a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept, the y-intercept represents the value of y when x equals 0.
In this problem, we have a relationship between the height of a tomato plant and the number of days since it has been planted. The height is the variable y, and the number of days is the variable x.
To find the y-intercept, we need to determine the value of y when x equals 0. However, in this table, there are no data points where x is zero, so we can't directly determine the y-intercept from the given data.
To find the approximate value of the y-intercept, we can use linear regression to find the equation of the line that best fits the data. Linear regression calculates the slope and y-intercept of a line that closely represents the relationship between the two variables.
Using statistical software or even a graphing calculator, you can input the given data points and perform linear regression analysis to find the equation of the best-fit line. The equation will be in the form y = mx + b, where m is the slope and b is the y-intercept.
Once the equation is obtained, you can determine the y-intercept by setting x to 0 and solving for y. That value will represent the approximate height of the tomato plant when it was first planted (0 days).
In summary, the y-intercept in this problem situation represents the approximate height of the tomato plant when it was planted (0 days), which can be determined using linear regression analysis.