Question

James planted a green bean seed and tracked its growth. After 2 weeks, the plant was 3 centimeters tall, and after 5 weeks, the plant was 18 centimeters tall. Fill in the missing information to find the rate of change and the initial value.

Characteristic

Calculation

1 Formula used to find the rate of change, m

Select Answer

2 Rate of change

Select Answer

3 Plugging values ​​into the slope-intercept form, y = mx + b, to solve for the initial value, b

Select Answer

4 Initial value

-7

Answer 1

1 Formula used to find the rate of change, m
m = (y2 − y1) / (x2 − x1)

2 Rate of change
m = (18 − 3) / (5 − 2) = 15 / 3 = 5 cm per week

3 Plugging values into y = mx + b to solve for b
Use (2, 3): 3 = 5(2) + b → 3 = 10 + b → b = −7

4 Initial value
−7 cm (value of b, the model's height at week 0)