Linear Equations
What makes a linear equation LINEAR?

An equation in one or more
variables, each with an exponent of
ONLY 1, where these variables are
only added or subtracted.
So with that definition Which of these
equations are linear?




x+y = 5
2x+ 3y = 4
7x-3y = 14
y = 2x-2
3

y=4





x2 + y = 5
x=5
y
xy = 5
x2 +y2 = 9
y = x2
So with that definition Which of these
equations are linear?
Linear




x+y = 5
2x+ 3y = 4
7x-3y = 14
y = 2x-2
3

y=4
Not Linear





x2 + y = 5
x=5
y
xy = 5
x2 +y2 = 9
y = x2
If you had to describe a line what
characteristics would you detail?
y
y
x
Line A
x
Line B
Slope, Intercepts
y
y
x
Line A
x
Line B
Slopes
Positive
Negative
Horizontal Vertical
Intercepts – where the line
crosses ythe axes.
y-intercept=4
x-intercept=-3
x
x
x-intercept=-5
y-intercept=-5
Line A
y
Line B
Intercepts are actually points in
the coordinate
system.
y
y
y-intercept=(0,4)
x-intercept=(-3,0)
x
x
x-intercept=(-5,0)
Line A
y-intercept=(0,-5)
Line B
Quadrants Review
y
II
I
x
III
VI
Ordered Pairs Review : (x,y)
y
(-x,y)
II
I
(x,y)
x
(-x,-y)
III
VI
(x,-y)
Linear Equations – What you should be
able to identify for all lines.
 The Equation Form
 Direction
 Slope
 y-intercept
 x-intercept
 Parallel Slope

Perpendicular Slope
Equation Forms
 Slope
Intercept
 Standard
 Horizontal
 Vertical
y = mx + b
Ax + By = C
y=b
x=a
Slope-Intercept
y = mx + b
m
 Slope
b
 y-intercept
y=½x+5
y = -3x - 7
Standard Form
Ax + By = C

A, B, C are all integers with A > 0
3x – 2y = 9
4x + 2y = 16
Given our 4 example equations identify all
of the following…







The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope
y=½x+5
2. y = -3x – 7
3. 3x – 2y = 9
4. 4x + 2y = 16
1.
y=½x+5







The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope
1.
2.
3.
4.
5.
6.
7.
Slope intercept
Rising
½
5
-5/(½) = -10
½
-2
y = -3x – 7







The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope
1.
2.
3.
4.
5.
6.
7.
Slope intercept
Falling
-3
-7
- -7/(-3) = -7/3
-3
-7
3x – 2y = 9







The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope
1.
2.
3.
4.
5.
6.
7.
Standard
Rising
3/2
-4.5 or 9/2
3
3/2
-2/3
4x + 2y = 16







The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope
1.
2.
3.
4.
5.
6.
7.
Standard
Falling
-2
8
4
-2
1/2
What if you are just given two points on a
line?

The slope formula
m=

y2 – y1
x2 – x1
Similar to Point-Slope Form
y – y1 = m(x – x1) or y2 – y1 = m(x2 – x1)
1st – Find the Slope:
y
A(6,6)
x
B(-3,9)
slope = (6 - -9)
(6 - -3)
=
y
15
=
9
3
A(6,6)
x
B(-3,9)
5
slope = (6 - -9)
(6 - -3)
=
y
15
=
9
3
A(6,6)
x
B(-3,9)
5
Now substitute the slope and one point
into the slope intercept form y = mx + b

m = 5/3 point (6,6)


6 = (5/3)(6 + b)
6 = 10 + (5/3)b
-4 = (5/3)b
-12/5 = b

Linear equation is y = (5/3)x – 12/3


31 Linear Equations
On – Line Assignment