Slope
Which variable in y = mx + b represents slope?
m
The knitting club is selling mittens for $7 and hats for $6. They earned $225. Let m represents mittens and h represents hats. Write an equation to model this situation.
225 = 7m + 6h
Is (1, 3) a solution to the following system:
2y = 8 - 2x
x = 2y - 5
Yes
Name any point that is on the line y = 3x - 5
Answers vary
Find the slope of the line that passes between the points (1, 1) and (4, 10).
m = 3
The soccer team is driving to their next game. Between the players and the families there are 90 people that need a ride. Some drivers have vans which fit 8 people, and others have cars which fit 5 people. Write an equation to represent how many cars, c, and how many vans, v, will be needed to drive everyone.
90 = 8v + 5c
Is (-1, 5) a solution for the following system:
14 = 3y + x
8x + 2y = -2
No
Name 2 points on the line 2y + 4x = 8
Answers vary
Find the slope of the line that passes between the points (3, 7) and (1, 3).
m=2
A high school club is researching a tour package offered by the Island Kayak Company. The company charges $35 per person and $245 for the tour guide. Which function represents the total cost, C, of this kayak tour package for x club members?
C = 245 + 35x
Solve the system:
2y = x + 5y = 7, x = 9
(9, 7)
What is the slope of the line that goes through (-2, 3) and (3, 1)
m = -2/5
What is the slope of the line that passes between
(0, 1) and (5, 2)?
m=1/5
Jim had a bag of coins. The number of nickels, n, and the number of quarters, q, totaled 28 coins. The combined value of the coins was $4.00. Write a system of equations that models this situation.
n + q = 28
0.25q + 0.05n = 4.00
Solve the system of equations:
4y - 2x = 14
x = 5
y = 6, x = 5
(5, 6)
Alex had $1.70 worth of nickels and dimes in his desk. There were 25 coins in all.
Write a system of equations that could be used to determine both the number of nickels, n, and the number of dimes, d, that Alex had.
d + n = 25
0.05n + 0.10d = 1.70
M=-2/3
Anna plans to spend $30 on balloons and party hats. Balloons cost $2 each and party hats cost $1.50 each. The number of party hats Anna needs is twice as many as the number of balloons.
If x represents the number of balloons and y represents the number of party hats, write a system of equations that can represent this situation.
30 = 2x + 1.50y
y = 2x
Solve the system of equations.
y = x + 2
12 = y + 4x
x = 2, y = 4
(2, 4)
Solve the system of equations.
4y + 3x = 10
y = 1
x = 2, y = 1
(2, 1)