Problem Solving with Slope

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, y, after x hours of service.

• Y = 50x + 25

• Y = 25x + 50

• Y = 50x - 25

• Y = 25x - 50

A fitness club opens with 80 members. Membership increases by 15 members per month. Which equation represents the relationship between the number of months the club has been opened, x, and the total fitness club membership, y?

• y=15x

• y=15x+80

• y=x+15

• y=80x+15

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

• y = 20x + 5

• y = -5x +20

• y=5x + 20

• y = 5x - 20

Decide if the following statements are true or false about the graph.

Groups:

(a) True

,

(b) False

• The slopes are equal, so the system has infinitely many solutions

• The lines are perpendicular which means they will not ever cross.

• The lines will eventually touch, so the system has one solution

• The line are parallel, so the system has no solution

• The lines will not intersect, so the system has no solution

• The slope(m) of the lines are equal

What does the slope represent on the graph?

• Dollars started in the savings account

• How many weeks they are saving

• The dollars saved per week

• The weeks it takes to save

Seth owns a printing shop that makes customized T-shirts. The cost to make T-shirts is proportional to the number of T-shirts he makes. Seth graphs a line that shows the cost per customized T-shirt. Two points on the line are (2, 4) and (5, 10). What does the slope of the line mean in this situation?

• The cost is $0.50 per shirt

• The cost is $2.00 per shirt

• The cost is $2.50 per shirt

• The cost is $6.00 per shirt

Yuki and Roman are photographers for the yearbook. Yuki starts with 50 photos. She then takes 30 photos each week. Roman starts with 84 photos. He then takes 28 photos each week. After how many weeks will Yuki and Roman have taken the same number of photos? Write a system of equations that can be used to solve the problem.

What is the equation for the savings account graphed? hint: y=mx+b m=slope b=y-intercept(starting spot)

Mathematical Equivalence

OFF

Scoots and Zooms are two scooter rental companies. (y = mx + b)·       Scoots charges $4 initial fee plus $5 per hour rental·       Zooms charges $2 initial fee plus $6 per hour rentalWrite the equations that will find when will the rental cost of the two companies be the same. ​ (a)   x + ​ (b)   = ​ (c)   x + ​ (d)   ​

• 5

• 4

• 6

• 2

• 8

• 2x

• 3x

If two equations have the Same Slope and the Same Y-Intercept, how many solutions do they have?

• Infinite

• No Solution

• One Solution

• Undefined