# Holiday Shopping!

### Which day is the best deal for you?

## It's That Time of Year....

## Variables

*x*represent the year.

Let* y* represent the number of products.

## Gifts Bought on Boxing Day Data Table

**Equation of Line***Slope and y intercept form: *

*y = mx + b*

*y = 30x + 200*

*Standard form:*

*Ax + Bx + C = 0 *

*30x + y + 200 = 0*

## Gifts Bought on Christmas Data Table

**Equation of Line***Slope and y intercept form: *

*y = mx + b*

*y = -50x + 900*

*Standard form:*

*Ax + Bx + C = 0*

*50x + y - 900 = 0 *

## Linear System Comparison

## Question

## Solution - Solving for a Point of Intersection

1. We can solve by graphing

Using the equations given for each line, we can graph each line using the y intercept and rise over run for slope.

**Christmas Sales **

*y = -50x + 900*

- (0,900) is the y intercept so plot it

- Then use rise over run to graph the slope which is -50

- Graph the line

**Boxing Day Sales **

*y = 30x + 200*

- Repeat same steps

Then, using the 2 graphed lines, find the point of intersection. On the graph, the point of intersection is in the year of 2008 with

2. You can also solve these linear systems by substitution (algebraically)

*y = -50x + 900*

*y = 30x + 200*

*Sub in one equation into the other and solve for x*

* -50x + 900* *= 30x + 200*

*900 - 200 = 30x + 50x*

*700 = 80x*

*700/80 = x *

*x = 8.75 *

*Now sub x back into any equation and solve for y*

*y = 30(8.75) + 200*

*y = 262.5 *

Therefore, the point of intersection is (8.75 , 262.5)

**Hence, in the year of 2008, there were 262 (262.5 to be exact) products sold on each day. **