Final answer:
To create a model for sunflower growth, calculate the slope using two points and use one of them to find the y-intercept. The y-intercept and x-intercept of the line represent the initial height and the theoretical heightless point, respectively.
Step-by-step explanation:
When creating a model that shows the relationship between the number of days a sunflower grows and its height, you would often use a scatter plot and draw a line of best fit. To create the equation of this line, you need two points to determine the line's slope.
Let's use the given points (15, 50) and (48, 135), which represent the number of days and the height of the sunflower in centimeters respectively.
To find the slope (m), use the formula m = (Y2 - Y1) / (X2 - X1), which would result in (135 - 50) / (48 - 15) = 85 / 33. Once you have the slope, you use one of the points to solve for the y-intercept (b) using the form y = mx + b.
Plugging the known values back in, we get 50 = (85/33)*15 + b which gives us the y-intercept after rearranging. The x-intercept occurs when y=0, so the equation 0 = (85/33)x + b is solved for x.
The y-intercept represents the starting height of the sunflower when the number of days is 0, while the x-intercept would theoretically represent the number of days at which the sunflower would not have any height, which isn't practically applicable in this scenario.