Relations & Functions
Slope & y-intercept
Linear Equations
Solving Systems of Linear Equations by Graphing
Solving Systems by Substitution
Word Problems
100
Is the relation a function?
[ ( 3 , 5 ), ( 4 , 7 ), ( 4 , 8 ), ( 6 , 10 ) ]
No, x = 4 shows up twice
100
Find the slope and y-intercept for the following equation:
y = 5x - 4
m = 5 & b = -4
100
Graph the line with the following characteristics:
slope = 3, going through the point ( 0 , -5 )
y = 3x - 5
100
Is the ordered pair ( 2 , 1 ) a solution for the system:
5x + 3y = 16 & -2x + 3y = -1
NO
100
Find the solution of the following equation for x = -3, 0, & 2:
y = 3x - 2
( -3 , -11 ), ( 0 , -2 ), & ( 2 , 4 )
100
The sum of two numbers is 30. Their difference is 12. Find the numbers.
21 and 9
200
Is the relation a function?
[ ( 0 , -1 ), ( 1 , 3 ), ( -2 , 4 ), ( 3 , 6 ) ]
Yes, no x-value repeats
200
Find the slope and y-intercept for the following equation:
2y = 3x + 12
m=3/2 & b=6
200
Graph the following linear equation:
y=1/2x-1
200
Is the ordered pair ( 2 , 1 ) a solution for the system:
2x + 3y = 7 & -3x + 2y = -4
YES
200
Solve by substitution:
−3x + 3y = 4
−x + y = 3
no solution
200
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
senior citizen ticket: $8, child ticket: $14
300
What is the capital of Ireland?
Dublin
300
What is the slope of the line that goes through the following points:
( 8 , 3 ) & ( -3, 1 )
m=2/11
300
Write the equation a line that passes through the point (-2,-8) and has a slope of 2.
y=2x-4
300
Solve the following system by graphing:
y = x + 3 & y = 3x - 1
SOLUTION: ( 2 , 5 )
300
Solve by substitution:
y = 6x − 11
−2x − 3y = −7
(2,1)
300
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?
35 hot dogs
52 sodas
400
Is the relation a function?
[ ( 1.5 , 6 ), ( 1.5 , 1.1 ), ( 1 , 1.9 ), ( 1 , 3.2 ) ]
No, x = 1.5 shows up twice
400
What is the slope of the line that goes through the following points:
( -6 , -7 ) & ( 3 , 5 )
m=4/3
400
Find the equation of a line that passes through the points (0,0) and (9,4).
y=4/9x
400
Solve the following system by graphing:
x+y=-7 & 3y - 3x = - 3
SOLUTION: ( -3 , -4 )
400
Solve by substitution:
−4x + y = 6
−5x − y = 21
(-3,-6)
400
You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?
$1.25 per soft taco
$2.50 per burrito
500
Is the relation a function?
Is the number of miles driven a function of the amount of gasoline used?
No, speed and type of car can affect the amount of gasoline used. Also sitting in traffic uses gas and not necessarily go anywhere.
500
A line passes through the points (3,-4) and (x,1). If the slope is 1/2, find the value of x.
13
500
Find the equation of a line that passes through the points (3,-3) and (-6,-3)
y=-3
500
Solve by graphing:
1/2y - x = 2
-10x+5y=20
infinitely many solutions
500
Solve by substitution:
−5x − 8y = 17
2x − 7y = −17
(-5,1)
500
The sum of twice a number and 4 times another number is 4. The first number decreased by the second number is 5. Find the numbers.
4 and -1