Unit 2—The Study of Linear Equations
What is slope?
Definition:___________________________________________
Two ways to know the slope of a line (we will learn more!):
Way #1: Count it out:
Way #2: Use the formula:
Given the points: (-2, 3) and (1, -1)
A POSITIVE SLOPE
A NEGATIVE SLOPE
ZERO SLOPE
UNDEFINED
SLOPE
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What is a linear equation?
These are linear equations:
These are NOT linear equations:
y=3x – 6
y – 2 = 3(x+4)
y + 2x – 2 = 0
5x = 4
=6
2x + y = 12
Can you give an example of a linear
equation?
y2 – 2 = 5
=y
3
=y
|2x+3| = 4
(x – 3)2 +4 = y
Can you give an example of something
that is NOT a linear equation?
We will be discussing linear equations in two forms:
Slope Y-intercept form
Standard form
y = mx + b
Ax + By = C
In this form…the “m” is the slope!
b is the y-intercept.
What is the y-intercept?
2
We can use this form to graph a line..
y = mx + b
We can use this form to graph a line…
ax + by = c
The X and Y Intercepts Method
Given: 2x – 3y = 6
 The Y-intecept is the point in the equation
where the X value is zero.
Using the equation substitute X = 0.
Slope Y-intercept Method
Find the Y value: 2x – 3y = 6
Given: 3x + y = -4

2(0) – 3y = 6
-3y = 6
Put equation into the y = mx + b form:
Y = -2
________________

The y-intercept is:_________.

Graph this point.
The ordered pair for this point is:_________.

The slope is:___________. This means:
The y intercept is -2.
The ordered pair is: (0, -2).
The X-intercept is the point in the equation

where the Y value is zero.
.

Using the equation substitute Y=O.
Count out the slope from the y-intercept.
Find the X value:
2x – 3y = 6
2x – 3(0) = 6
2x = 6
x=3
The x intercept is 3.
The ordered pair is: (3,0)

Graph these two intercepts and connect the
two points.
3
Find the slope:
#1.
#2.
#3. (4, 6) (-3, 0)
Graph these lines using slope y-intercept:
#4. y = 3x
#5. y = − x + 1
Graph these lines using x and y intercepts.
#6. 2x – 4y = − 8
#7. x + 3y = 9
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