3.6 - Equations
of Lines in the
Coordinate Plane
Please view the presentation in
slideshow mode by clicking this
icon
at the bottom of the
screen.
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
𝟐
x
𝟑
What is the graph of y = + 2?
***The equation is in slope-intercept𝒓𝒊𝒔𝒆
form, y = mx + b.
𝟐 for
TIP
2
***The slope is m =
___
andusing
the y-intercept
is
b
=
___.
𝒓𝒖𝒏
𝟑
UP
for positive or
DOWN for negative.
Step 1: Graph Rise
the y-intercept
Step 2: Find another
point using
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
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.
𝑟𝑖𝑠𝑒
m=
=
𝑟𝑢𝑛
5 −3
=
3 −−5
2
1
= =
8
4
Equation:
Using
Using
𝑦2 − 𝑦1
𝑥2 − 𝑥1
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