Question

An experimental gardener decides to plant seeds to grow a fruit tree. the seeds are planted 3 inches into the ground. according to the research, the tree is expected to grow around 12 inches each year. a linear model can be used to note the height of the fruit tree. write a linear model in slope-intercept form to model this situation. use x to represent the independent variable.

Answer 1

The linear model for the growth of the fruit tree in slope-intercept form is y = 12x + 3, where x is the time in years, and y is the height of the tree in inches.

To write a linear model in slope-intercept form (y = mx + b) for the situation described, where a fruit tree grows roughly 12 inches each year and is initially planted 3 inches into the ground, we first identify our independent and dependent variables. The independent variable x will represent the time in years, and the dependent variable y will represent the height of the tree in inches. Since the tree starts at 3 inches tall, that is our y-intercept (b). The slope (m) is the growth rate, which is 12 inches per year.

Therefore, the linear model will be y = 12x + 3.