Algebra 1
Functions – Equations in two variables
Warm up:
1. Let the rule f(t) represent the number of people, in millions, who own cell phones t years after 1990.
Explain the meaning of the following statements.
a.
f(10) = 100.3
b. f(a) = 20
c. f(20) = b
2. Use the graph below to mark specific points indicated by the statements below. Label the coordinates of any
points you draw.
a. f(0) = 2
b. f(-3) = f(3) = f(9) = 0
c. f(2) = g(2)
d. g(x) > f(x) for x > 2
e. g(0) = 0
3. For each table, determine whether the relationship is a “Function” or “Not a function.” Then, either write the
function rule or explain why the relationship is not a function.
x
-1
0
-1
2
3
n
y
-15
-9
-3
3
9
Expression
x
-4
0
2
8
10
n
y
-19
-7
-1
17
23
Expression
4) Sales Job. Prime Products will pay you a weekly salary of $100 plus 10% of sales. Show how your weekly
earnings is a function of your sales.
a) Create a table, graph and write a rule using function notation, that makes sense for this situation. Label your
axes with the appropriate variables for this situation
Sales
($/wk)
0
1000
2000
3000
4000
5000
6000
Function rule:
Earnings
($/wk)
𝐸(𝑠) =
b) What do you think is a practical domain and range for this situation?
Using the function rules you wrote above, evaluate the following. After you evaluate, explain what your
solution means relative to the situation.
c) 𝐸(700) =
d) 𝐸(8000) =
e) 𝐸(ℎ) = 3500
Algebra 1
Graphing/Writing Equations in Slope-Intercept Form
3
1. On the grid below, graph the equation 𝑦 = 2 𝑥 − 3. First, identify its slope and y-intercept to help you
with the graph.
Slope:__________
y-intercept: __________
2. Write down two points this line passes through and use
them to calculate the average rate of change of this
function.
3. Rewrite each of the following linear equations in equivalent 𝑦 = 𝑚𝑥 + 𝑏 (slope-intercept) form.
Identify the slope and the y-intercept and then graph on the grid given. Label each line with its original
equation.
(a) 2𝑥 − 3𝑥 = 10
Slope: _________
y – intercept: _________
(b) 𝑥 + 2𝑦 = 6
Slope: _________
y – intercept: _________
(c) 3𝑦 + 12 = 5𝑥
Slope: _________
y – intercept: _________
4. Consider the linear function whose graph is shown at the right.
(a) Determine an equation in the form 𝑦 = 𝑚𝑥 + 𝑏 for this line.
(b) Test your equation for the value 𝑥 = 2.
When the y-intercept is an integer, such as in the last exercise, it is fairly easy to get the exact relationship
between x and y. Let’s try another graphical problem where the y-intercept is not an integer.
5. Find the equation of the linear function shown in slope-intercept form.
Test your equation for 𝑥 = −4.
We need to also be able to find the equation for a linear function if we know two points that lie on it.
6. Find the equation of the line that passes through each of the following pairs of points in 𝑦 = 𝑚𝑥 + 𝑏 form.
(a) (2,5) and (5, 17)
(c) (-1,11) and (4,-4)
7.
(b) (-2,5) and (2,3)
(d) (3,4) and (12,19)
Li Na is saving money. Her parents gave her an amount to start, and since then she has been putting
aside a fixed amount each week. After six weeks, Li Na has a total of $82 made of her own savings in
addition to the amount her parents gave her. Fourteen weeks from the start of the process Li Na has
$118. Using w for the number and weeks and S for the amount in savings (in dollars) construct a linear
function that describes the relationship between the number of weeks and the amount of savings.
Interpret what the slope and y intercept mean, relative to the situation.