5.1-5.3b More Linear Equations
Algebra 1
As a group, answer the following questions. Make sure everyone has the same answers and
understands their answers before moving on. Show all of your work.
Activity 1: Given a graph….
1.
The graph to the left is the graph of a
walk-a-thon situation. The scale on both
axis is 1 (meaning every square represents
“1”). Label your graph.
a. Fill out the table to the right.
b. What is the y-intercept? What does it
represent in this situation?
Miles
walked
Money
collected
x
y
0
1
2
3
4
c.
5
What is the slope? What does it represent
in this situation?
d. Write an equation that best models this situation.
e.
Does this situation represent a direct variation? Why or why not?
Activity 2: From a table…
a. The table represents a record of how much someone has saved. What is
the y-intercept? What does it represent?
b. What is the slope? What does it represent?
c.
Write an equation using function notation that best models this
situation.
d. Graph your equation on the coordinate grid to the
right. Because you are graphing the equation, not just
your data, your graph should be a line, not a series of
points.
e.
If this table and graph modeled a walk-a-thon
situation, how much did they collect in donations?
f.
How much would they be making for each mile
walked?
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Number of
weeks
Money
total
x
y
0
1
1
4
2
7
3
10
4
13
Activity 3: Start with an equation…
The equation y = -3 + 2x models a child selling tickets for a juggling show to their friends.
The only expense was the juggling balls.
a.
What is the y-intercept and what
does it represent?
b. What is the slope and what does it
represent?
c. Fill in the values on the given table.
d. What is the x-intercept and what
does it represent?
f. Graph the linear equation on the coordinate grid provided.
Even though this is discrete data because you can’t sell
partial tickets, your graph can be a line because you are
graphing the equation on which the points lie.
Activity 4: Another Equation…
This is the function for the height of a hot air balloon
over the ground while it descends (meters per second):
f(x) =
a.
3
18 - x
2
Why would it make sense to create a table with an xscale of 2?
b. What is the y-intercept and what does it represent?
c.
What is the x-intercept and what does it represent?
d. What is the slope and what does it represent?
e.
Graph the hot air balloon equation on the coordinate grid
provided. Label.
f.
Is this a discrete or continuous situation?
Activity 5: Given Two Points…
Using points (0,5) and (2,0)
a. What is the y-intercept?
b. Fill out the table.
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x
0
1
2
3
4
5
y
2
Activity 6: Given very little information….
The function is in direct variation. The dependent variable y, is in terms of twice the
independent variable x.
a. Write an equation.
b. Write a possible situation that this could represent.
c.
What is the slope? The y-intercept? The x-intercept?
More on the back!
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Activity 7: Review Vocabulary...
Fill in the following blanks using the vocabulary from the investigation:
Continuous
Dependent
Direct Variation
Discrete
Domain
Independent
Linear
Negative
a.
Parallel
Parent Function
Positive
Range
Rate of Change
Rise over Run
x-intercept
y-intercept
Y when x = 0
The part of the “y = “ equation that is the coefficient of x is the same as the
__________________ on the table and the __________________on the graph.
b. The part of the “y = “ equation that is the constant is the same as the _________________ on
the table and the __________________ on the graph.
c.
A line that goes through the origin represents a ___________________________.
d. A graph that is increasing has a slope that is a __________________ number, a graph that is
decreasing has a slope that is a __________________ number.
e.
The ____________________variable goes on the x-axis and the _____________________
variable goes on the y-axis.
f.
When you are finding a break-even point in a situation, you look for the ________________ on
the graph.
g.
When values between data points are possible, it is a called a __________________ situation.
If there are no values between points possible, it is a ___________________ situation.
h. y=x or f(x)=x is called ____________________________.
i.
The graphs of equations with different y-intercepts, but the same slope, are _____________.
j.
All possible x-values of a function are called the ______________. All possible y-values of a
function are called the ______________________.
k.
A _________________________ function is created by a constant rate of change.
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