Question

1. lynn is tracking her trees growth. on the second day, it is 6.5 cm and the plant grows 1.5 cm a day.

what information is given?
write an equation in point - slope form:
change your equation to slope - intercept form:
use your equation to answer the following question:
how tall is the tree after 9 days?

Explanation:

Part 1: Identify Given Information

• Slope (Growth Rate): The plant grows at a rate of \( 1.5 \, \text{cm/day} \), so the slope \( m = 1.5 \).
• Point: On the 2nd day (\( x = 2 \)), the height is \( 6.5 \, \text{cm} \) (\( y = 6.5 \)). Thus, the point is \( (2, 6.5) \).

Part 2: Point - Slope Form

The point - slope formula is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1)=(2, 6.5) \) and \( m = 1.5 \).

Substitute the values:
\( y - 6.5 = 1.5(x - 2) \)

Part 3: Slope - Intercept Form (\( y=mx + b \))

Start with the point - slope equation:
\( y - 6.5 = 1.5(x - 2) \)

1. Distribute the slope:

\( y - 6.5 = 1.5x-3 \)

1. Solve for \( y \) by adding \( 6.5 \) to both sides:

\( y=1.5x - 3+6.5 \)
\( y = 1.5x+3.5 \)

Part 4: Height After 9 Days

Use the slope - intercept equation \( y = 1.5x+3.5 \), where \( x = 9 \) (days).

Substitute \( x = 9 \):
\( y=1.5(9)+3.5 \)

1. Calculate \( 1.5\times9 \):

\( 1.5\times9 = 13.5 \)

1. Add \( 3.5 \):

\( y=13.5 + 3.5=17 \)

Final Answers:

• Given Information: Slope \( m = 1.5 \), point \( (2, 6.5) \).
• Point - Slope Form: \( \boldsymbol{y - 6.5 = 1.5(x - 2)} \)
• Slope - Intercept Form: \( \boldsymbol{y = 1.5x+3.5} \)
• Height After 9 Days: \( \boldsymbol{17 \, \text{cm}} \)

Answer:

Part 1: Identify Given Information

• Slope (Growth Rate): The plant grows at a rate of \( 1.5 \, \text{cm/day} \), so the slope \( m = 1.5 \).
• Point: On the 2nd day (\( x = 2 \)), the height is \( 6.5 \, \text{cm} \) (\( y = 6.5 \)). Thus, the point is \( (2, 6.5) \).

Part 2: Point - Slope Form

The point - slope formula is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1)=(2, 6.5) \) and \( m = 1.5 \).

Substitute the values:
\( y - 6.5 = 1.5(x - 2) \)

Part 3: Slope - Intercept Form (\( y=mx + b \))

Start with the point - slope equation:
\( y - 6.5 = 1.5(x - 2) \)

1. Distribute the slope:

\( y - 6.5 = 1.5x-3 \)

1. Solve for \( y \) by adding \( 6.5 \) to both sides:

\( y=1.5x - 3+6.5 \)
\( y = 1.5x+3.5 \)

Part 4: Height After 9 Days

Use the slope - intercept equation \( y = 1.5x+3.5 \), where \( x = 9 \) (days).

Substitute \( x = 9 \):
\( y=1.5(9)+3.5 \)

1. Calculate \( 1.5\times9 \):

\( 1.5\times9 = 13.5 \)

1. Add \( 3.5 \):

\( y=13.5 + 3.5=17 \)

Final Answers:

• Given Information: Slope \( m = 1.5 \), point \( (2, 6.5) \).
• Point - Slope Form: \( \boldsymbol{y - 6.5 = 1.5(x - 2)} \)
• Slope - Intercept Form: \( \boldsymbol{y = 1.5x+3.5} \)
• Height After 9 Days: \( \boldsymbol{17 \, \text{cm}} \)