Station 1
A gym charges a $75 fee to sign up.
It costs $42 per month to belong to the gym.
a) Write an equation that gives the total cost (c) of belonging to the
gym as a function of the number of months (m) that you have
belonged to the gym.
b)
Sketch a graph of the function. Label your axes.
Station 1 key
a)
b)
c = 42m + 75
see graph below (you only need the first quadrant)
Station 2
Identify the key features of the function that passes through the points
(7 , 2) and (-2 , 5).
(no decimal answers)
Key feature
Slope
x-intercept
y-intercept
Zero of the function
Answer
Station 2 key
Key feature
Slope
Answer
−
1
3
x-intercept
(this needs to be a
coordinate point)
(13,0)
y-intercept
(this needs to be a
coordinate point)
(0,
Zero of the function
13
3
)
The zero of the function is
the same as the value of the
x-intercept. The zero of the
function is 13 or (13,0).
Station 3
The linear function, f(n), has the same y-intercept as 4x – 3y = 10
and the same slope as 2x – 8y = 12.
a)
b)
Write the equation of f(n) in slope-intercept form.
Identify the x and y intercepts of f(n).
Station 3 key
The linear function, f(n), has the same y-intercept as 4x – 3y = 10 and the same slope as 2x – 8y = 12.
a)
Write the equation f(n) in slope-intercept form.
Same y-int as 4𝑥 − 3𝑦 = 10
Same slope as 2𝑥 − 8𝑦 = 12
−3𝑦 = −4𝑥 + 10
−8𝑦 = −2𝑥 + 12
4
10
3
3
𝑦= 𝑥−
so the y-int is (0, -
10
3
𝟏
𝟏𝟎
𝟒
𝟑
So 𝒇(𝒏) = 𝒙 −
b) Identify the x and y intercepts of f(n).
x-intercept: The x-intercept is the point where y=0
1
10
𝑥−
4
3
10 1
= 𝑥
3
4
40
40
= 𝑥 so the x-intercept is ( 3 , 0)
3
0=
y-intercept: (0, -
10
3
) already found that in part a
1
3
1
4
2
4
𝑦 = 𝑥 − so the slope is
)
Station 4
a) Explain how to tell if a function is direct variation by looking at the following:
1. Table
2. Graph
3. Equation
b) The vacation time of an employee in hours (v) varies directly with the number of hours they
work (w). An employee who works 100 hours earns 1.5 hours of vacation time.
1. What two points do you know are on the graph of this function?
2. What is the slope of this function?
3. Write a direct variation equation that relates v and w.
4. Using the equation, how many hours of vacation time does an employee earn after working
325 hours?
Station 4 key
1. Table – DV can be seen on a table because x and y are only related by multiplication or
division
2. Graph – DV can be seen on a graph because the line goes through the origin
3. Equation – DV can be seen on an equation because the y-int is zero
The vacation time of an employee in hours (v) varies directly with the number of hours they
work (w). An employee who works 100 hours earns 1.5 hours of vacation time.
1. (0,0) and (100 , 1.5)
3
2. m = 200 (don’t leave decimals in your fraction)
3
3. v = 200w
4. v =
975
=
200
195
40
=
39
8
7
= 48 hours
Station 5
a) Write equations in Point-slope form and Slope-intercept form for the linear
function f with the given values. f (-1) = 8 , f (3) = 10
b)
Write the equations of the horizontal and the vertical lines that pass
through the point (-9 , 6).
Horizontal:
Then identify their slopes.
Vertical:
Station 5 key
a) Point-slope form –
Slope-intercept form –
1
y – 10 = (x – 3)
2
1
17
2
2
y= x+
b) Horizontal: y = 6 (slope is 0)
1
OR y – 8 = (x + 1)
2
Vertical: x = -9 (slope is undefined)
Station 6
You have $10 to spend on snacks from a vending machine,
and you decide to spend it all. (YOLO!)
Some snacks are 50 cents and some are 25 cents.
a) Write an equation in standard form that shows the combinations of 0.50 and 0.25 snacks you
can buy.
Consider the following:
Is there more than one way to write the equation? Why or why not?
What should you remember about standard form?
b) Graph your equation
Consider the following:
Which quadrants do you need?
What is a quick method to use to make the graph?
Is it possible to have more than one graph for this situation?
Station 6 key
You have $10 to spend on snacks from a vending machine you decide to spend it all. (YOLO!) Some snacks are 50 cents and some are 25 cents.
a) Is there more than one way to write the equation?
YES BECAUSE THE BOTH 50 CENT AND 25 CENT SNACKS COULD EITHER REPRESENT X OR Y – DEFINE YOUR
VARIABLES TO BE CLEAR. YOU COULD ALSO WRITE AN EQUIVALENT FORM OF THE STANDARD EQUATION.
What should you remember about standard form? COEFFICIENTS MUST BE INTEGERS!
Standard form: 50x + 25y = 1000 (if x = #50 cent snacks and y = # 25 cent snacks)
This can also be written as 2x + y = 40
b) Which quadrants do you need? ONLY THE FIRST QUADRANT BECAUSE WE CAN’T HAVE NEGATIVE SNACKS
What is a quick method to use to make the graph? USE INTERCEPTS
Is it possible to have more than one graph for this situation? YES, IF YOU HAVE DEFINED YOUR VARIABLES IN THE OTHER WAY.
*Remember, too that this is really a discrete function, but in order to see all possibilities for x and y we connect the intercepts.*
Station 7
Write the point-slope form, slope-intercept form, and standard form of the equation of the line that
passes through the point (-4 , 5) and has a slope of 6.
point-slope form:____________________________
slope-intercept form: _________________________
standard form:______________________________
Station 7 key
Write the point-slope form, slope-intercept form, and standard form of the equation of the line that
passes through the point (-4 , 5) and has a slope of 6.
point-slope form: y – 5 = 6 (x + 4)
slope-intercept form: y = 6x + 29
standard form: 6x – y = -29 (we usually write standard form with the first coefficient positive)