# Unit 1 * Foundations of Algebra

```Unit 2 – Linear Equations &amp;
Inequalities
Topic: Writing &amp; Graphing Linear
Functions
Materials needed for notes:
Pencil &amp; paper
Flip book
Journal
Things I expect you to remember
from Algebra 1 that I do not explain
in this PowerPoint
Slope-intercept form of a linear equation.
 Graphing a linear function given:

A point on the line &amp; the slope of the line.
 The function of the line in slope-intercept form.

Using the slope formula (I will give you the formula
in a couple slides, but I expect you to remember how
to use it).
 Using the graph of a line to write a function in
slope-intercept form.

Things you should remember from
Algebra 1 but that I KNOW you need
to be reminded of
Identifying a linear function from data.
 Standard form of a linear equation.


Recognizing standard form &amp; graphing a line given a
function in standard form.
The equations for horizontal &amp; vertical lines.
 Using data to write a linear function in slopeintercept form.
 The relationship in the slopes of parallel &amp;
perpendicular lines.

Formulas for Linear Functions (put
these on a note card)


Slope formula

(x1, y1) &amp; (x2, y2) are coordinates for 2 points on the line

A, B, C  R, A &amp; B cannot both be 0
y2  y1
m
x2  x1
Standard form of a linear function
Ax  By  C

Point-slope form of a linear function


x1, y1 represent the coordinates of a point on the line
Can be used to find the equation of a line in slope-intercept given slope
&amp; a point, or two points
y  y1  m( x  x1 )
Identifying Linear Functions From
Data


Linear functions have one &amp; only one output value for
every input value.
Rate of change (slope) between dependent variable and
independent variable is constant.
Identifying Linear Functions From
Data
x
f(x)
0
-1
2
2
+3
+2
+2
+2
4
8
+6
6
17
+9
Rate of change is not constant. Data represents a function,
but not a linear function.
Identifying Linear Functions From
Data
x
f(x)
-2
3
0
3
+0
Rate of change 
+2
+2
+2
2
3
+0
4
3
+0
f ( x) 0

Rate of change is constant. Data represents a linear
x
2 function.
Identifying Linear Functions From
Data
x
f(x)
-3
3
-1
0
1
-3
-1
-6
Two different outputs for the same input. Data does not represent a function.
Graphing Linear Functions in
Standard Form

Use standard form to determine x- &amp; y-intercepts.



Set y = 0 &amp; solve for x to find x-intercept.
Set x = 0 &amp; solve for y to find y-intercept.
Plot the intercepts and graph the line they form.
Horizontal &amp; Vertical Lines

Horizontal lines have m = 0



No rise, just run
y-value is constant so
equation is always y = b,
where b = y-intercept
Example: write the
equation for the given line

y=5
Horizontal &amp; Vertical Lines

Vertical lines have
undefined slope



Rise, but no run (can’t divide
by 0)
x-value is constant so
equation is always x = a,
where a = x-intercept
Example: write the
equation for the given line

x = –7
Parallel &amp; Perpendicular Lines

Parallel Lines


Two lines whose slopes are equal.
Perpendicular Lines


Two lines whose slopes are negative reciprocals.
The product of the slopes of perpendicular lines is -1.

EXCEPTION: A horizontal line (m = 0) is perpendicular to a vertical
line (m is undefined).
JOURNAL ENTRY


TITLE: Checking My Understanding: Writing
&amp; Graphing Linear Functions
Review your notes from this presentation &amp;
create and complete the following



“Things I already knew:” Identify any information
with which you were already familiar.
“New things I learned:” Identify any new
information that you now understand.
“Questions I still have:” What do you still want to
know or do not fully understand?
Homework
Textbook Section 2-3 (pg. 110): 22-40
even
 Textbook Section 2-4 (pg.121): 12-18
even, 19-22
 Due 9/6 (B day) or 9/7 (A day)

```