Understanding Proportional Relationships
What is Rate of Change?
Rate of Change is a comparison of two quantities that are changing.
Solve for x.
2(3x + 0.5) = 25
x = 4
What are a system of linear equations?
A system of equations is a set of two or more linear equations that have the same variables.
What is the substiution method?
Using the substiution method, you solve one equation for one of the variables, and then substitute the expression equal to the variable into the second equation.
What is the slope-intercept form?
y = mx + b
The unit rate is a ratio of measurements in which the second measurement is 1.
Simplify the expression on the right side of the equation by applying the distributive property
4 - 2k = -5(k + 7)
k = -13
Solve the system of linear equations graphically
y = -x = 2
y = 1/2x + 4
The solutions of the system of equations is (-4,2).
Solve the system of linear equations by substitution.
x - 2y = 7
3x + 4y = -9
The solution to the system of equations is (1 , -3)
A pool is being drained so that it can be repaired. The graph shows the amount of water in the pool during the time it takes to drain to completely. Write the functions that is represented by the graph.
The function represented by the graph is y = -750x + 6000. The rate of change is -750 gallons per hour. The initial value is 6000 gallons
For the past month, Mr. Stumm recorded the number of days he went to work each week. He also recorded the number of tollbooths he drove through during those days. Mr. Stumm drove the same route to and from work each day. How many tollbooths does Mr. Stumm drive through each day?
Use the table to find the unit rate of the data
Number of days | Number of Tollbooths
3 12
6 24
7 28
Mr. Stumm goes through 4 tollbooths per day
Solve for y.
3/4(4y + 8) 5 + 3y
The equation has no solution
Solve the system of linear equations
2x + y = 6
4x + 2y = 0
The system of equations has no solutions
What is the elimination method?
The elimination method is when you can add or subtract the two equations to eliminate one of the variables.
What is a relation?
A relations is a set of ordered pairs
Allyson mows lawns to make extra money. The equation 30x - 2y = 0 compares the amount of money Allyson earns, y, to the number of lawns she mows, x. How much does Allyson earns for each lawn she mows?
Allyson earns $15 for every lawn she mows.
Solve for x.
10c - 6(2c - 1) = -2(c - 3)
The equation has infinitely many solutions
What are parallel lines?
Parallel line have the same slope but different y- intercepts.
Solve the system of linear equations by elimination.
5x + 4y = 7
x + 4y = -5
The solutions to the system of equations is (3 , -2).
What is a function?
A function is a relation in which each input has exactly one output.
Compare the equation y = 1/4x to the table. Do the have the same slope?
x | y
0 0
3 3/4
5 1 1/4
8 2
Yes, They have the same slope because they both equal 1/4x
Mr. Williams is buying tickets for the school musical. Adult tickets cost $3 more than student tickets. He buys 7 student tickets and 6 adult tickets, and he spends a total of $83. What is the price of one adult ticket?
The price of one adult ticket is $8
What are coincident lines?
Coincident lines have the same slope and the same y-intercept
Solve the system of linear equations algebraically. Check your solution by graphing the equations.
6x + 3y = 14
3x + 2y = 10
The solutions to the system of equations is (-2/3 , 6)
What is the vertical line test?
The vertical line test says that if a vertical line can be drawn so that it passes through more than one point on the graph