Expressions & Equations
Simplify: 4x + 7 + 2x − 3
6x + 4
Define function.
What is a function is a mathematical relationship where each input has exactly one output?
Identify the y-intercept of the equation y = 5x − 4.
-4
Classify the solution as one solution, no solution or infinitely many solutions: x + 1 = x + 4
No Solution
A movie ticket costs $8 plus a $2 service fee. Write an equation for the total cost y for x tickets.
y = 8x + 2
Solve for x: 3x + 5 > 20
x > 5
Determine whether the relation is a function: (1, 3), (2, 5), (3, 7), (4, 9)
It is a function
What is the slope of the line passing through (1, 2) and (3, 6)?
2
The graph of two lines intersects at (−1, 5). What does this point represent?
It is the solution to the system because it satisfies both equations.
A gym charges a $25 sign-up fee and $15 per month. Write the equation.
y = 15x + 25
Solve: 5(x − 2) = 3x + 6
x = 8
Is the following relation a function? Explain. (2, 5), (2, 8), (3, 9)
No, because the input 2 has two different outputs.
Write the equation of a line with slope of 3 and y-intercept of 2
y=3x+2
Find the solution to this system:
y = x + 2
y = −x + 6
(2,4)
Two friends are saving money. Friend A starts with $20 and saves $5 each week. Friend B starts with $50 and saves $2 each week. Write the two equations.
Friend A: y = 5x + 20
Friend B: y = 2x + 50
A student solved the equation 4x + 2 = 4x + 9 and got x = 7. Explain why this is incorrect.
They have the same coefficient, therefore it does not have a solution because 2 does not equal 9
Does the linear equation y = 4x - 5 represent a proportional or non-proportional relationship?
A line passes through the points (0, −1) and (4, 7). Write the equation of the line.
y = 2x − 1
Find the solution to this system:
2x + y = 9
y = x + 3
Using the equations below, determine after how many weeks the friends will have the same amount.
y = 5x + 20
y = 2x + 50
10 weeks
Solve for h: A=1/2bh
What is h=2A/b?
What is the difference between a proportional and non-proportional relationship?
A proportional relationship passes through the origin and is in y=mx form while a non-proportional relationship doesn't pass through origin, has a non-zero y-intercept and is in y=mx+b form.
Compare the steepness of Line A and Line B. Line A is defined by the equation y = 2x + 5, and Line B passes through the points (9, 8) and (0, 1). Which line is steeper? Justify your answer using their slopes.
Line A because line A's slope is 2 while Line B's slope is 7/9. 2 > 7/9
Create a system of equations with infinitely many solutions.
Answers may vary
A taxi company charges $3 to start and $2 per mile. Another taxi company charges $7 to start and $1 per mile. At how many miles will the cost be the same?
4 miles