3.6 - Equations
of Lines in the
Coordinate Plane
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Warm Up
Substitute the given values of m, x, and y into the equation y
= mx + b and solve for b.
1. m = 2, x = 3, and y = 0
2. m = –1, x = 5, and y = –4
Solve each equation for y.
3. 4x – 2y = 8
y = 2x – 4
b = –6
b=1
Objectives
Graph lines and write their equations in slope-intercept and
point-slope form.
Classify lines as parallel, intersecting, or coinciding.
For Instance…
How can you use the
THINK…
(5,4)
EXAMPLE
1:
y-coordinates
to get the rise
(1,2)
If
you
don’t
have
a
of
2
units?
1) What is the slope of the line?
Subtract!
how could you
6
5 −−1 graph,
4 – 2the
= 2coordinates
= use
5
3 −−2
How can you find the run of 4 units?
(x,y)
to find the rise
Subtract!
2) What is the
the line between the points (4, -6) &
5 –slope
1 and
= 4of run?
(7,2)?
2 − −6
8
=
7 −4
3
EXAMPLE 2: Graphing Lines
using slope-intercept form

x

What is the graph of y = + 2?
***The equation is in slope-intercept
form, y = mx + b.
 for
TIP
2
***The slope is m =
___
andusing
the y-intercept
is
b
=
___.


UP
for positive or
DOWN for negative.
Step 1: Graph Rise
the y-intercept
Step 2: Find another
point using


for
But ALWAYS Run to the m = 2. Go up 2, and
3
RIGHT!
over 3. *REPEAT*
Step 3: Draw a
line through the
points with
arrows.
Step 1: Find the
slope between the
two points.
Writing Equations
of Lines:
The y-intercept is not
Given 2 Points
clear from this picture,
can’t use slopeWhat issoanweequation
of the line in the
intercept form, we’ll
figure athave
thetoright?
use point-slope
form.

m=
=

5 −3
=
3 −−5
2
1
= =
8
4
Equation:
Using
Using
2 − 1
2 − 1
Step 2: Choose any
one point as (x1, y1).
1
(-5,3): y – 3 = (x + 5)
4
1
(3,5): y – 5 = (x – 3)
4
…or…
Step 3: Insert m, x1,
and y1 into the
point-slope equation.
Equations of Horizontal and Vertical Lines
HORIZONTAL LINE:
0
Horizontal lines have a slope of ____.
Let’s look at some
Every point on the horizontal line
points
on the
through (2, 4) has
a y-coordinate
of
Horizontal Line
4
____.
The equation of the line is ________.
y=4
(-2, 4) (0, 4)
VERTICAL LINE:
undefined
Vertical lines have
slopeatofsome
_____.
Let’salook
Every point on the
vertical
line
points
on the
through (2, 4) has an x-coordinate
Vertical Line
2
of _____.
x=2
The equation of the line is _________
(3, 4) (5, 4)
(2,2)
(2,0)
(2,-1)
Horizontal Lines:
y=#
Vertical Lines:
x=#
Example 3A: Classifying Pairs of Lines
Determine whether the lines are parallel, intersect, or
coincide.
y = 3x + 7, y = –3x – 4
The lines have different slopes, so they intersect.
Example 3B: Classifying Pairs of Lines
Determine whether the lines are parallel, intersect, or
coincide.
Solve the second equation for y to find the slope-intercept form.
6y = –2x + 12
Both lines have a slope of
lines are parallel.
, and the y-intercepts are different. So the
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Lines in the Coordinate Plane