Question

3. A group of workers is harvesting berries at a constant rate. An equation that represents the number of baskets of berries the workers picked over a period of time, in hours, is y = 2x + 15. (a) What are the slope and the y-intercept for the equation that represents the number of baskets of berries the workers picked over a period of time? (b) What are the rate of change (slope) and the initial amount (y-intercept)? Explain the meaning of the rate of change and the initial amount for the situation. Answer in complete sentences

Answer 1

In y = mx + b form, the slope can be found in the m position and the y intercept can be found in the b position.

y = mx + b

y = 2x + 15

slope(m) = 2 and y int (b) = 15

The initial amount is the y intercept, which is 15. The rate of change (the slope) is 2

example :  

baskets picked in 1 hr :

y = 2(1) + 15

y = 2 + 15

y = 17

baskets  picked in 2 hrs :

y = 2(2) + 15

y = 4 + 15

y = 19

so the slope ( rate of change) is basically saying for every hr of picking, you pick 2 baskets...so your picking 2 baskets per hr.

The y intercept (15) is telling us that they already had 15 baskets to start with.