Question

PLEASE HELP ME FILL OUT NUMBER 2 I DID THE OTHER QUESTIONS FOR YOU TO USE

1) The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average rate of 3/4 foot per year.

a) Write an equation in Slope-Intercept form to represent the growth of the trees over time. Let x represent the number of years and let y represent the height (in ft.) of the tree.

Y=3/4x+3

b) What does the y-intercept represent in your equation

Stands for feet Y=3

c) Determine the height of the tree in 3 years.

Y=3/4×3+3=9/4+3=21/4=5.25 feet

2. Could the equation 3x - 4y = - 12 be used to represent the same information in question #1? Explain your reasoning

a) What does the 3 and the 4 in this equation tell us?

b) Using this equation can you tell me how tall the tree will be in 24 years?

c) Using the equation find the x-intercept. What does this mean in this problem?​

Answer 1

The equation you provided for the growth of the trees over time, Y=3/4x+3, is in slope-intercept form and can be used to represent the information provided in the problem.

a) The y-intercept in the equation, represented by the constant 3, stands for the initial height of the trees when they are planted (3 feet tall). The slope of the line, represented by the coefficient of x (3/4), represents the average rate of growth of the trees over time (3/4 foot per year).

b) In 3 years, the height of the trees can be found by substituting 3 for x in the equation and solving for y: Y=3/4*3+3=9/4+3=21/4=5.25 feet.

The equation 3x - 4y = - 12 cannot be used to represent the same information in question #1 because it is not in slope-intercept form. In order to be in slope-intercept form, the equation must have the form y = mx + b, where m represents the slope and b represents the y-intercept.
a) The 3 and 4 in the equation 3x - 4y = - 12 represent the coefficients of the x and y terms, respectively. They do not represent the initial height or the rate of growth of the trees.

b) It is not possible to determine the height of the trees in 24 years using the equation 3x - 4y = - 12 because it is not in the correct form.

c) The x-intercept of the equation 3x - 4y = - 12 can be found by setting y equal to 0 and solving for x: 0 = 3x - 4y, so x = - 4y/3. This means that the x-coordinate of the point where the line intersects the x-axis is - 4y/3. This has no meaning in the context of this problem, as the x-axis represents the number of years and the y-axis represents the height of the trees.

Answer 2

1)

a) The equation Y=3/4x+3 can be used to represent the growth of the trees over time.

b) The y-intercept in this equation represents the starting height of the trees, which is 3 feet.

c) In 3 years, the height of the trees will be 5.25 feet according to the equation.

2)

No, the equation 3x - 4y = -12 cannot be used to represent the same information in question #1. This equation is not in slope-intercept form, which is necessary to represent a linear relationship between two variables.

a) The 3 and the 4 in this equation are coefficients of the variables x and y, respectively. They do not represent any specific value or quantity in the context of the problem.

b) It is not possible to determine the height of the tree in 24 years using this equation because it is not in the correct form.

c) To find the x-intercept, we can set y to 0 and solve for x. This gives us x = -3. The x-intercept in this equation represents the number of years at which the height of the tree is 0 feet. This does not have any meaning in the context of the problem.