Talking About Change
Identify the independent and dependent variables:
Does the amount of time you spend studying affect your final grade?
Independent - time studying
Dependent - final grade
How do you know if a graph shows a linear relation?
It is a straight line.
State the slope (ROC) and initial value of the line:
d = -7t - 45
m = -7, b = -45
6x + 19 = 43
x = 4
The equation of Line A is y = 15x + 27.
Line B has an initial value that is 5 more and a rate that is 3 less. Write the equation for Line B.
y = 12x + 32
Identify the independent and dependent variables:
Is there a relationship between a person's age and their fitness level?
Independent - age
Dependent - fitness level
State the general equation of a line.
y = mx + b
State both equations for slope (ROC).
m = rise/run
m = change in y/ change in x
-7 + 4x = 45
x = 13
The cost of hosting a party at a hall is made up of a one-time fee of $2000 plus $170 per guest. Determine an equation relating the cost, C, in dollars, and the number of guests, n.
C = 170n + 2000
Identify the independent and dependent variables:
A graph is labelled Time on the x-axis and Height on the y-axis.
Independent - Time
Dependent - Height
Which line has a higher initial value?
Line A: y = -5x + 3
Line B: y = -7 + 2x
Line A
Determine the rate of change and initial value.
x y
0 100
10 250
20 400
30 550
m = 15, b = 100
-2x + (-12) = -52
x = 20
The height of an aircraft, in feet, after t minutes is given by the equation: h = 3000 - 500t
Is the height of the aircraft increasing or decreasing? Why?
Decreasing because slope (ROC) is negative.
Fill in the blank: A straight line that slants upward has ___________ rate of change.
a) increasing
b) decreasing
c) constant
d) no
c) constant
Which line is steeper?
Line A: y = 1 - 4x
Line B: y = 2x - 5
Line A
Determine the rate of change and initial value.
m = -750, b = 4500
x - 10x - 3 = 151 + 8
x = -18
A gym charges a one-time registration fee of $75 plus a monthly membership fee of $50. What is the cost of being a gym member for 5 months?
$325
A graph shows y, the height in feet of a ball, at x seconds after it was thrown. What unit would be used to describe the ball's rate of change?
feet per second (ft/s)
Is the following relation linear or non-linear? Why?
x y
0 2
1 6
2 10
3 14
4 18
Linear because increasing at a constant rate of 4 (first differences = 4)
Ryan is saving money to buy a new bike. He has some money saved and will add a constant amount each week.
After 3 weeks he has $120. After 5 weeks he has $180.
How much money does he add each week (what is the rate of change)?
$30 per week
(6x + 9) - (2x - 11) = 28
x = 2
The volume of liquid, in litres, in a container after t minutes is given by the equation: V = 5t + 8. After how many minutes does the container hold 23 litres of liquid?
3 minutes