Create a word problem with two linear equations. One equation is a proportional relationship and the other is not a proportional relationship. Interpret the meaning of the slope and y
-intercept in context. Work with a partner. Have one person create a proportional relationship in an equation format, table, and a graph. Have the other person find the unit rate or slope for each format. Then reverse the roles.
Word problem:
Alice and Bob are both running a lemonade stand. Alice sells lemonade for $1 per cup, while Bob sells lemonade for $2 per cup. However, Bob also charges a $5 entry fee to the stand. Let x represent the number of cups of lemonade sold and y represent the total cost for each stand.
Equation for Alice (proportional relationship):
y = 1x
Equation for Bob (not a proportional relationship):
y = 2x + 5
Table:
For Alice:
x | y
1 | 1
2 | 2
3 | 3
For Bob:
x | y
1 | 7
2 | 9
3 | 11
Graphs:
(Graph for Alice would be a straight line passing through the origin with a slope of 1)
(Graph for Bob would be a straight line passing through the point (0,5) with a slope of 2)
Interpretation of the slope and y-intercept:
For Alice, the slope of 1 indicates that for every cup of lemonade sold, the total cost increases by $1. The y-intercept of 0 indicates that there is no fixed cost.
For Bob, the slope of 2 indicates that for every cup of lemonade sold, the total cost increases by $2. The y-intercept of 5 indicates that there is a fixed cost of $5, which is the entry fee to the stand.