Parallel and Perpendicular Lines
The slopes of two perpendicular lines are....
A.) the same
B.) opposite reciprocals
B.) opposite reciprocals
Is the following coordinate point an X intercept or Y intercept?
(0,9)
Y-intercept
Solve the equation for the specific variable
a-q=a+sx for x
-q/s
Solve the systems of equations below
2x+5y=20
6x+15y=15
no solution
17≥x-9
x ≤ 26
Write an equation in slope-intercept form for a line that is parallel to the line y=-5x-3 and has a y-intercept of 6.
y = -5x + 6
What is the y-intercept and the slope of the following equation?
y = 5x +10
Slope = 5
y-intercept = 10
Solve the equation for the specific variable.
a-q=a+sx for q
q = −sx
Solve the systems of equations below
5x+4y=22
6x+y=15
(2, 3)
-3x≤-9 or 6x-1<5
x ≥ 3 or x < 1
Write an equation in slope-intercept form for a line that is perpendicular to the line y=-5x-3 and has a y-intercept of 6.
y = 1/5x + 6
-2/3x+y=-4
What is the y intercept of the equation?
(0,-4)
Teddy has 23 boxes of juice packed and plans to pack 3 additional boxes each hour. Charley has 7 boxes of juice packed and plans to pack 5 additional boxes each hour. The equation below represents when Teddy and Charley will have packed the same number of boxes, based on x number of hours.
23 + 3x = 5x + 7
After how many hours will Charley have packed the same number of juice boxes as Teddy?
8 hours
Paws at Play made a total of $1,234 grooming 22 dogs. Paws at Play charges $43 to groom each small dog and $75 for each large dog.
Write a system of equations that can be used to determine the number of small and large dogs that were groomed.
S + L = 22
43S + 75L = 1234
where S is the number of small dogs and L is the
number of large dogs groomed
7<3x-5≤22
4 < x ≤ 9
Write an equation in standard form for a line that is parallel to the line with an equation of y= 3x -5 that passes through the point (8,5).
-3x + y = -19
-2/3x+y=-4
What is the rate of change (slope) of the equation?
2/3
There are a total of 36 cards in Aleera’s collection. The number of baseball cards is 6 less than twice the number of football cards. X represents the number of football cards.
a.)Write an equation that represents the situation, where x represents the number of football cards.
b.)How many baseball cards does Aleera have?
a. x + (2x − 6) = 36
b. 22 baseball cards
Chapman’s brickyard sells bricks and blocks. A brick costs $0.38 and a block costs $1.56. The brickyard filled a $24.80 order, which contained 28 items.
Write a system of equations that can be used to find the number of bricks and blocks in the order.
x + y = 28
0.38x + 1.56y = 24.80
where x is the number of bricks and y is the
number of blocks
A gym charges its members a one-time $10 sign-up fee, and $25 per month. Samantha has at most $185 to spend.
a.)Write a one-variable linear inequality that Samantha could use to determine how many months she can attend the gym.
b.)Solve the inequality and represent the solution both algebraically.
a.185 ≥ 25x + 10 ≥ 0
b.7 ≥ x ≥ 0
Write an equation in standard form for a line that is perpendicular to the line with an equation of y= 3x -5 that passes through the point (8,5).
1/3x + y = 23/3
-2/3x+y=-4
What is the x intercept of the equation?
(6,0)
The perimeter of a triangle is 84 meters. The longest side of the triangle is 7 meters less than twice the length of the shortest side, x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle?
21m, 28m, 35m
The ballpark made a total of $15,000 from ticket sales at Wednesday’s game. The ticket prices are $20 for an adult and $10 for a child. They sold 3 times as many children’s tickets as adult tickets.
Write a system of equations that can be used to determine the number of adult and child tickets sold.
20a + 10c = 15000
3a = c
where a is the number of adult tickets and c is the
child tickets
Palm Tran offers a monthly QuikPass which cost $55 for unlimited rides. If it cost $2 a single ride, for what number of rides would the QuikPass be less expensive?
28 rides or more