Question

1. 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 = 5x + 10.
(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 and the initial amount? Explain the meaning of the rate of change and the initial amount for the situation.



(c) Use graph paper to draw a graph representing the situation. Label the axes appropriately.

Answer 1

Answer: (a) The slope of the line is 5 and the y-intercept is (0,10). (b) The rate of change is 5 and the initial amount is 10.

Explanation:

The given equation is,

$y=5x+10$     .... (1)

(a)

The slope intercept form of the a line is,

$y=mx+b$      .... (2)

Where, m is slope and (0,b) is y-intercept.

On comparing (1) and (2) we get,

$m=5, b=10$

Therefore, the slope is 5 and the y-intercept is (0,10).

(b)

The rate of change is also known as slope therefore the rate of change is 5.

To find the initial amount put x=0 in the given equation.

$y=5(0)+10=10$

Therefore, the initial value is 10.

The rate of change represents the number of baskets of berries the workers picked increased by 5 units per unit of time.

The initial amount shows the number of  baskets of berries the workers picked before the workers starts harvesting.

(c)The graph is shown below.

Since x represents the time in hours, therefore x is always greater that or equal to 0.

Answer 2

Answer:

a) Slope, m = 5

Y-intercept, c = 10

b) The rate of change represents the number of baskets of berries the workers picked increased by 5 units per unit of time.

The initial amount is 10 that is 10 baskets were picket in the starting of harvest.

Step-by-step explanation:

We are given the following in the question:

An equation that represents the number of baskets of berries the workers picked over a period of time.

$y = 5x + 10$

a) Comparing the given equation to the point slope form of straight line,

$y =mx +c$

where m is the slope and c is the y-intercept that is the value of y when x is zero.

Slope, m = 5

Y-intercept, c = 10

b) Rate of change is the slope of the given equation.

The rate of change means how the output is changing as the input changes.

The rate of change is the slope which is 5.

In this case we can interpret the rate of change as The rate of change represents the number of baskets of berries the workers picked increased by 5 units per unit of time.

The initial amount shows the output when the input is zero that is the number of  baskets of berries the workers picked before the workers starts harvesting.

It is represented by y-intercept.

The initial amount is 10 that is 10 baskets were picket in the starting of harvest.

c) The attached image shows the graph for the given equation.