Lines and Linear Equations
Graphs
Equations
Word Problems
Linear Relations
100
In y= 3x - 893, what is the rate of change and initial value?
Rate of Change is 3
Initial value is -893
100
This graph shows the cost to rent a banquet hall for different numbers of people.
The owner decides to raise the fixed cost of the hall to $200 and raise the cost of a meal to $30/person.
Which describes the new relation between cost to rent the hall, C, and the number of people, n
The initial value moves to 200. The rate of change changes to 30 so the line gets steeper. The new equation is C = 200 + 30n.
100
Y=3x +45 Where x = 4. What is Y.
What is 57
100
Estimate a value beyond it's given set of values.
extrapolate
100
The coordinates of a graph are as followed (2,2), (4,4) (6,6) (8,8) is this a linear relation.
Yes
200
6x = 36. What is the value of x?
6
200
Mark made this graph that shows the value for different numbers of loonies.
Sue wants to make a similar graph to show the value for different numbers of toonies.
Which describes the new relation between the value, V, of toonies and the number of toonies, nn
The initial value does not change. The rate of change changes to 2 so the line gets steeper. The new equation is V = 2n.
200
A statement that two mathematical expressions are equal and have the same value.
What is equation.
200
Halley's comet appears approximately every 76, since the year 1758. What year will it be when it appears for the 3rd time?
1910
200
(22,55), (88,165), (166,205), (44,110). Is this a linear relation?
No
300
V=5000-100h
What is the rate of change/slope?
-100
300
The graph shows the cost Sherri will pay to do some kite sailing.
What amount she will pay for 6 h?
180
300
The cost of renting an airplane is $210 in airport taxes and an extra $1.20 per kilometre travelled. Which equation below represents the relationship between the cost of a rental (C) and the distance flown in kilometres (d)?
C = 1.20 + 210
300
A school pays $125 to design gym T-shirts. It costs an additional $25 to make each T-shirt. How much would it cost to make 25 T-shirts?
$750
300
A relation that is a straight line when graphed is called a?
Linear relation
400
y = 5x +100
y= 3x +200
Which line has a steeper slope?
y= 5x +100
400
Describe Sean's trip to school.
Sean walks quickly to school, gets tired and slows down. Realizes he is late and runs the rest of the way.
400
A pool starts with 6000L of water and drains at a rate of 200L per minute. What is the equation?
V=6000-200t
400
A school pays $125 to design gym T-shirts. It costs an additional $25 to make each T-shirt. If the school has $5000 to spend on t-shirts, how many shirts can be made?
195
400
An equation whose graph is a not a straight line.
Non-linear
500
y = -1/3x + 4
y= -4/5x + 3
What line has a steeper slope?
y= -4/5x + 3
500
Ali started walking quickly to class when he realized that he forgot his book at his locker. He slowed down then turned around and went back to his locker increasing his speed as he walked. Then he ran the rest of the way to class at a constant rate.
Draw a sketch of distance time graph to represents Ali's walk to class
500
One carpenter has to cut 50 pieces of wood, and he can cut 4 pieces per hour. A second carpenter has to cut 62 pieces of wood, and he can cut 7 pieces per hour. They start cutting wood at the same time. What is the relationship between the combined number of pieces left to be cut between the two carpenters (N)(N) and the number of hours (h)(h) that have elapsed since they started cutting?
N=112 - 11h
500
This equation represents the relationship between the number of dogs (D) adopted at a dog shelter in a week, and the number of volunteers (v) who post adoption ads around the neighborhood.
D=17+8v
Based on this equation, how many dogs does each volunteer help find a home for?
8
500
X, 1, 2 , 3, 4, 5
Y,1.2, 2.4, 3.6, 4.8. 6.0
What is the Rate of change/slope?
m = 1.2