Question

Kristin bought two sunflower plants. Plant A is 8 inches tall and is growing at a rate of 3 inches per week. Plant B is 12 inches tall and is growing at a rate of 2 inches per week. Write the two equations to represent each sunflower plant if the plants to continue to grow at the same rate. In your equations, x represents the number of weeks, and y represents the height of the plant in inches. (1 point) Plant A: y= Plant B: y= Question 2 When will the plants be exactly the same height? This question requires you to show your work. (1 point) The plants will be exactly the same height during week .

Answer 1

To create the equations for each sunflower plant:

**Plant A:**
The height of Plant A after \( x \) weeks can be represented by the equation:
\[
y = 8 + 3x
\]
where \( 8 \) is the initial height and \( 3 \) is the growth rate in inches per week.

**Plant B:**
The height of Plant B after \( x \) weeks can be represented as:
\[
y = 12 + 2x
\]
where \( 12 \) is the initial height and \( 2 \) is the growth rate in inches per week.

### Summary of the equations:
- Plant A: \( y = 8 + 3x \)
- Plant B: \( y = 12 + 2x \)

### To determine when the plants will be the same height:
Set the two equations equal to each other:
\[
8 + 3x = 12 + 2x
\]

Now, solve for \( x \):
1. Subtract \( 2x \) from both sides:
\[
8 + 3x - 2x = 12
\]
which simplifies to:
\[
8 + x = 12
\]

2. Subtract \( 8 \) from both sides:
\[
x = 12 - 8
\]
simplifying gives:
\[
x = 4
\]

Therefore, the plants will be exactly the same height during week **4**.