1. Solving Linear Equations by Graphing
Section 3.2
Solving Linear Equations by Graphing

2. Linear equations have at most
root:
a ________; any value that makes the equation _____.
solution
true
Linear equations have at most
_____ ______.
one
root
Linear Equation
Related Function
3x – 6 = 0
y = 3x – 6
f(x) = 3x – 6

3. Solve 3x – 6 = 0 (Algebraically):
3x = 6
x = 2
solution
____ is the __________ of 3x – 6 = 0 2

4. Solve 3x – 6 = 0 (Graphically):
Graph y = 3x – 6
x y = 3x – (x, y)
(–1, –9) 1
3(–1) – 6 = –3 – 6 = –9
(0, –6)
x-intercept
3(0) – 6 = 0 – 6 = –6
(1, –3) 1
3(1) – 6 = 3 – 6 = –3 2
x-intercept
__ is the ___________ of y = 3x – 6 2
__ is the ___________ of f(x) = 3x – 6
root

5. Solve ½ x + 3 = 0 (Algebraically):
Clear the denominator.
2(½ x) + 2(3) = 2(0)
x + 6 = 0
–6 –6
x = –6
____ is the __________ of 3x – 6 = 0 –6
solution

6. Solve ½ x + 3 = 0 (Graphically):
Graph y = ½ x + 3
x y = ½ x (x, y)
(–2, 2) 2
½(–2) + 3 = –1 + 3 = 2
(0, 3)
x-intercept
½(0) + 3 = = 3
(2, 4) 2
½(2) + 3 = = 4 -6
x-intercept
__ is the ___________ of y = ½ x + 3 -6
__ is the ___________ of f(x) = ½ x + 3
root