Post Secondary Test Prep Day 15 Vocabulary and Practice Notes
1. Setting up a linear equation.
You'll need to know how to set up a linear equation given a word problem.
There are three things you need to identify: the variable, variable change, and constant.
Take a look at this example:
Here, our variable is the number of weekly payments, 𝒘.
The variable change is the amount associated with 𝒘, which
is the weekly cost of $30. And our constant is $60 because it
doesn't change each week - it's just the upfront payment.
So, the total price of $300 is equal to the constant plus the
added-up weekly payments: 300 = 30𝑤 + 60.
2. Graphs of linear equations.
You'll also need to know how to define a linear equation from a graph and how to graph a linear
equation. Here's an example:
Based on the graph, you need to figure out the equation
of the line. We do this by identifying the slope and the
y-intercept. The y-intercept is the easiest one - it's the
value of y the line crosses the vertical y-axis at. In this
case, it's -4.
The slope is the change in y divided by the change in
𝑥 between two points In this case, it's -1.
Our line is then y = -x - 4, which is equivalent to Choice C.
Practice
1.
During the first three months of its life, a breed of exotic fish is born with one stripe and then
develops two new stripes every five days. What is the number of stripes, s, that the fish has at t days
after its birth?
a.
2.
2
t =5 s
b. s = 5t + 1
2
c. s = 5 t + 1
5
d. s = 2t + 1
Which equation best matches the graph of the line shown below?
a.
y−2=4(x−4)
b.
y+2=4(x−4)
c.
y−2=4(x−4)
1
1
d. y+2=4(x−4)
3.
Which of the following points does the line y=
a.
(14, 25)
b. (-5, -3.5)
c. (2, 7)
3
x+4 NOT pass through?
2
d. (6, 12)
Day 15 HW Practice Sheet Understanding Linear Representations Name____________________
Practice 1.
The cost to rent a tandem bike at the boardwalk includes a flat fee of $20 plus a charge of $4.50
for every half hour of use. Which of the following functions describes the total cost, in dollars,
for a rental lasting x hours?
a. C(x) = 9x + 20
b. C(x) = 4.5x
c. C(x) = 29x
d. C(x) = 4.5x + 20
Practice 2.
A silk-screening company charges $150 to create a printing screen from your artwork and print a
minimum of 25 T-shirts. Each additional shirt is $5. Write an equation to represent the cost of t
T-shirts over 25 T-shirts.
Practice 3.
Cherie is going to a charity book sale at her local library. Every book costs 40 cents, but only
after you pay $8 to enter the sale. Which of the following functions describes the total dollar
amount that Cherie will spend at the library to take home b number of books?
a.
C(b) = 8 + 40b
b. C(b) = 8 + 0.40b
c. C(b) = 0.40 + 8b
d. C(b) = 8.40b
Practice 4. Refer to the line in the diagram below. It we were to continue to
draw it so that it intersects the y-axis, where would its y-intercept be?
a.
3
5
(0,−2 )
2
3
b. (0,−1 )
2
5
c. (0,−1 )
1
3
d. (0,−1 )
Practice 5.
Line l includes the points (7,4) and (−3,4). Line k includes the points (8,−4) and (5,−4). Which of the
following statements is true of these lines?
a.
b.
c.
d.
e.
The lines are distinct but neither parallel nor perpendicular.
The lines are identical.
The lines are parallel.
Insufficient information is given to answer this question.
The lines are perpendicular.
Practice 6.
An individual's maximum heart rate can be found by subtracting his or her age from 220. Which graph
correctly expresses this relationship between years of age and maximum heart rate?
A.
B.
C.
D.