Holiday Shopping!
Which day is the best deal for you?
It's That Time of Year....
Variables
Let y represent the number of products.
Gifts Bought on Boxing Day Data Table
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
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.