# Pop vs. Water sales

### By: Saumya Naik

## The Situation

## Variables

Y (dependent) - Bottles sold (thousands)

## Water Sales

## Water

- y2-y1 / x2-x1 = slope
- 350-300 / 2-1 = slope (sub in given points)
- 50 / 1 = slope
- 50 = slope

Find the value of b using y=mx+b form

- y=mx+b
- y=50x+b
- 300= 50 (1) + b (sub in one point to find the value of b)
- 300= 50+b
- 300-50=b
- 250= b

**Therefore equation is y=50x+250**

*note this is in thousands

## Pop Sales

## Pop

- y2-y1 / x2-x1 = slope
- 1260 - 1340 / 2-1 = slope (sub in given points)
- -80 / 1= slope
- -80 = slope

Find the value of b using y = mx+b form

- y=mx+b
- y= -80x + b
- 1340 = -80(1) + b (sub in one point to find the value of b)
- 1340= -80 +b
- 1340 + 80 = b
- 1420 = b

**Therefore the equation is y= -80x +1420**

*note this is in thousands

## Graph

## Intersection Point

Using the graph above we can conclude that the lines intersect. On the graph you can see that the lines intersect on the point (9,700). Meaning that in the 9th month (September) that store sold an equal number of pop and water, 700.

Method 2: Substituting

Equations:

-80x+ 1420 = 50x+ 250

-80x - 50x = 250 - 1420

-130x = -1,170

x = -1,170 / -130

x= 9

Now use one equation to find the value of y.

y= mx + b

y= 50(9) + 250

y= 450 +250

y= 700

Therefore you know that the points intersect at (9, 700).

## Conclusion

Are people choosing a healthier drink?

Yes people are choosing the healthier drink (water) over the sugar filled drink (pop). Looking at the graph you can tell that over the year the number of water bottles sold is increasing while the number of pop bottles sold is decreasing, making water the more wanted choice.