# 11.4: Graphs of Linear Equations ```Module 4
Lesson 7
What values of x and y make this
equation true?
y  2x  7
There are infinitely many solutions!
Definition of Linear Equation
 A linear equation is an equation which has:
 one or two variables
 the variables appear in separate terms
 each variable occurs only to the first power
line
 The graph of a linear equation is always a _______.
 Which of these are linear equations? Why or why not?
y=x+1
35 = xy
y=–5
3p + 5q = 16
s = 0.2t
y = x2 + 7
Steps to Graph a Linear Equation
Choose at least three x-values and make a table of values.
2. List the solutions as ordered pairs.
1
3. Graph the ordered pairs.
y  x 3
2
4. Draw a line through them.
1.
x
-2
0
2
4
y=&frac12;x–3
y
Try this
x
-1
0
1
2
y=x+4
y=x+4
y
Try this
x
-1
0
1
2
y = –2x + 3
y = –2x + 3
y
Try this
x
-1
0
1
2
y = –5
y = –5
y
Day 2 :
Review Table of Values and
Graphing
Real-World Example
You are filling up your hot tub with water. It is currently at 4 gallons
and fills at 5 gallons a minute.
Write and graph an equation using the variables:
g: total gallons of water
m: time (in minutes)
0
2
4
6
g
2 46
m
gallons
g = 5m + 4
1
2
3
4
5
6
time (minutes)
7
8
Complete a table of values and graph
y = 3x – 2
x
y
x–y=6
x
y
Complete a table of values and graph
y=3
x
y
x = –7
x
y
```