A
Explain how you can tell on a graph whether a function is linear or not.
It makes a straight (non-horizontal*) line
Write an equation of a line that is parallel to
y = -1/2x + 10
Answers may vary, slope of -1/2 and y-int of not 10
What is the domain of the line y=x?
(-inf, inf) or all real numbers
What is the slope of the line that passes through (1, -5) and (3, 10)?
7.5
Name the three methods of solving systems that we have learned.
Graphing, Elimination, Substitution
Vertical stretch by a factor of 5, vertical translation up 2.
What is the slope of a line perpendicular to
y = 3x + 2?
-1/3
Is the function y=5 linear? Explain your reasoning.
[Answers may vary. But it is clearly not linear.]
Sometimes, always, or never true: a system of linear equations has two solutions.
Sometimes (!)
Find the y-intercept of the following function:
3x + 5y = 150
30
Graph the line y = -3/2(x + 3) - 1
(on board)
Sometimes, always, or never true:
The inverse of linear functions are linear.
Always
Write the equation of the line on the board:
y = 1/3(x + 4) - 2
What is the slope of the line 3x + 5y = 150?
-3/5 or -0.6
Find the x-intercept of the following function:
3x + 5y = 150
50
Write an equation in POINT-SLOPE form:
Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week.
y = 25(x - 0) + 100
Solve the system:
5x + y = 9
10x − 7y = −18
(1, 4)
Solve the system:
−3x + 3y = 4
−x + y = 3
no solution
Graph the line: 4x - 3y = 15
(on board)
Write a system of equations to model the following:
Rent-A-Car rents compact cars for a fixed amount per day plus a fixed amount for each mile driven. Benito rented a car for 6 days, drove it 550 miles, and spent $337. Lisa rented the same car for 3 days, drove it 350 miles, and spent $185.
337 = 6d + 550m
185 = 3d + 350m
Write a system of linear equations that has the solution (10, 2).
Answers may vary
Solve the system:
-x + 2y - 5z = -4
-4x + 9y +z = 5
3x +2y - 5z = -8
(-1, 0, 1)
How many stars are in our solar system?
one
Write an equation in STANDARD form:
You figured out that you could make $50 per pool to clean pools during the summer. You did, however, need to purchase some equipment to get started. After cleaning 3 pools you still were down a total of 15 dollars.
50x - y = 165