Systems
Solve the system of equations.
y=2x+1
y=x+4
(3,7)
Is this a function?
(1,4), (2,7), (3,10), (4,13)
Yes
A right triangle has legs that measure 6 inches and 8 inches.
What is the length of the hypotenuse?
10 inches
3(2x - 5) = 4(x + 1)
Which of the following is a linear equation?
A. y = 3x + 5
B. y = x^6 +4
C. y = sqrt x +2
D. y = 1/x +7
A: 3x+5
Solve the system of equations.
3x+2y=12
3x-2y=4
(8/3,2)
What is the slope and y-intercept?
Y-intercept is 5
A right triangle has a hypotenuse of 13 cm and one leg that measures 5 cm.
What is the length of the other leg?
12 cm
5x + 7 - 2x = 3x + 1
7=1
no solution
(0,2), (1,4), (2,6), (3,8)
Are these linear or non linear?
Linear, rate of change is constant
A movie theater sells adult tickets for $8 and student tickets for $5. A total of 10 tickets were sold for $62.
Which system of equations could be used to find the number of adult tickets a and student tickets s?
8a+5s=62
A gym charges a $20 sign-up fee and $15 per month.
Write a function rule to represent the total cost C after m months.
y=15x+20
A ladder leans against a wall. The bottom of the ladder is 9 feet from the wall, and the ladder reaches 15 feet up the wall.
How long is the ladder?
The ladder is approximately 17.5 feet long
x/3 +2 =x/6 +5
x=18
Non-linear because linear lines are straight
Two lines are graphed on a coordinate plane and intersect at the point (3, -1).
What does the point (3, -1) represent in the context of a system of equations?
The point (3, -1) represents the solution to the system, meaning it is the values of x and y that make both equations true.
Function A: y=4x+1
Function B: (0,3), (1,9), (2,15), (3,21)
Which has the greatest rate of change?
Function B
The side lengths of a triangle are 7, 24, and 25. Is this a right triangle?
Yes, it is a right triangle
2(3x - 4) + 5 = 4x + 7
X=5
A car rental company charges $40 per day plus a one-time fee of $100. Is the function describing total cost linear or nonlinear?
Linear, constant increase of $40
Solve the system.
y=-2x+6
4x+2y=12
Infinite solutions
y=2x^2 -3
29
Point A is located at (2, 3) and point B is located at (8, 15).
What is the distance between points A and B?
≈ 13.4 units
4(x - 2) + 6 = 4x - 2
4x-2=4x-2
Infinite solutions
Which of these is nonlinear?
A. 2x+5y=10
B. y=3x-7
C. y= x^3 +2
D. 4x-y=8
C due to x^3