Algebra II
Unit 1 – Handout 9 – Linear Functions in One Handout
This is a recap of about two units of Algebra I in one handout. So strap on your crash helmets.
Here we go!
We need to make sure we can all …
Not even close
Maybe a little
I got this
I can convert functions rules to and
from all three different forms.
I can graph a line given only the
function rule in any of the three
different forms.
Given a graph of a line, I can construct
the function rule in any of the three
different forms.
Given a graph of a line OR a function
rule (in any of the three different
forms), I can figure out the slope and
intercepts of the linear function.
Given a table of input values and
function values, I can figure out
whether or not the values represent a
linear function.
Given a table of input and function
values of a linear function, I can figure
out the function rule.
You’re going to need these:
LINEAR FUNCTION – A function that has a constant rate of change.
SLOPE – A measurement of the rate of change of a linear function.
Y-INTERCEPT – f(0), the function value when x = 0.
X-INTERCEPT – f(x) = 0; the x-value when the function value is zero.
Slope-Intercept Form
3 Forms of Linear Functions
Point-Slope Form
Standard Form
f(x) = mx + b
y - y1 = m(x – x1)
Ax + By = C
x = input variable
f(x) = function value
m = slope
b = y-intercept
x = input variable
y = output variable
m = slope
(x1, y1) = sample point
x = input variable
y = output variable
A (constant) ≠ 0
B, C (constants) could be any real #
Unit 1 – Handout 9 – Linear Functions in One Handout
Part I: For each of the following graphs of linear functions, identify:
a. The slope
b. The x- and y- intercepts
c. The equation in all three forms
Algebra II
Algebra II
Unit 1 – Handout 9 – Linear Functions in One Handout
Part II: On a piece of graph paper, using NO technology except your pencil, paper, and ruler, graph
each of the following linear functions.
1.
2.
3.
4.
5.
6.
f(x) = 2x + 3
(y – 3) = ½(x + 2)
5x + 3y = 15
x - 2y = 8
(y + 6) = -3(x – 4)
f(x) = (2/3)x – 4
Part III: Given each table of values, determine whether or not the table represents a linear function.
Explain your decision. If it is a linear function, find the function rule (in whatever form is the easiest
for you.)
1.
2.
3.
x
2
5
8
11
f(x)
9
17
25
33
x
3
9
15
21
f(x)
1
4
10
19
x
2
3
4
5
f(x)
0
1
2
1
x
-3
-1
1
3
f(x)
1
1.5
2
2.5
x
-3
-1
1
3
f(x)
1.5
1
.5
0
x
10
15
20
25
f(x)
-2
-7
-12
-17
4.