Geometry
Lesson 3 – 4
Equations of Lines
Objective:
Write an equation of a line given information about the graph.
Solve problems by writing equations.
Equation Forms
Slope-Intercept Form
y
= mx + b
 m – slope
 b – y-intercept
Point-Slope Form
– y1 = m(x – x1)
 m – slope
 (x1, y1)
y
Write an equation in slopeintercept form of the line with
slope 3 and y-intercept of –2.
Then graph the line.
y = mx + b
y = 3x – 2
Graphing:

Put a dot on the y-intercept


(0, 3)
Use slope (rise/run) to find more points.

Up 3 over 1
Write an equation in slope-intercept
form of the line with slope ½ and yintercept of 8. Then graph the line.
y=½x+8
Graphing
 Graph
(0, 8)
 Up 1 over 2
Don’t have to go by 2’s
Write an equation in point-slope
form of the line with slope –3/4
that contains (-2,5). Then graph.
y – y1 = m(x – x1)
3
y  5   x  2
4
(x – (-2))
Graphing: plot point, then use slope
Write an equation in point-slope
of the line with slope of 4 that
contains (-3, -6). Then graph.
y + 6 = 4(x + 3)
Write an equation of the line through
each points in slope-intercept form
(0, 3) and (-2, -1)
Method 2:
Find the slope
Method 1:
Find the slope


m=2
Use slope-intercept form



Pick one of the points
3 = 2(0) + b
b=3
y = 2x + 3
m=2
Use point-slope form


Pick one of the points
y – 3 = 2(x – 0)
Solve for y to put in
slope-intercept form.


y – 3 = 2(x – 0)
y – 3 = 2x
y = 2x + 3
You may use either method
Write an equation of the line through
each points in slope-intercept form
(-2, 4) & (8, 10)
4  10
6 3
m


 2  8  10 5
3
4    2  b
5
6
4
b
5
3
26
y  x
5
5
6
 4  b 6  20  b b  26
5
5 5
5
Write an equation of the line
through (-2, 6) & (5, 6) in slopeintercept form.
Find the slope

m = 0 (horizontal line)
6 = 0(-2) + b
6=b
y = 0x + 6
y=6
Make sure you simplify.
Do not leave 0x or 0
Horizontal & Vertical Lines
When an equation only has 1 variable it
is either a horizontal or vertical line
The equation tells you how to graph.
y=6
 The line goes through the axis of the
variable given.
 A horizontal line at 6 through the y-axis.

Tell whether the following is a
horizontal or vertical line.
y = 3 horizontal
x = 6 vertical
x = -1 vertical
5=y
horizontal
-9 = x
vertical
x=0
Vertical (y-axis)
y=0
Horizontal
X-axis
Write an equation in slope-intercept
form for a line perpendicular to the
line y = -3x + 2 through (4, 0).
Step 1: Identify slope for new equation

m = 1/3 (because of perpendicular)
Write new equation with new slope and point.

1
0  (4)  b
3
4
0  b
3
4
 b
3
1
4
y  x
3
3
Write an equation is slopeintercept form for a line parallel
to y = (-3/4)x + 3 containing (-3, 6)
Step 1: Identify slope for new equation

(-3/4) same slope since parallel
Write new equation with new slope and point.
9
3
6   (3)  b 6   b
3
15
4
4
9
6  b
4
15
b
4
y  x
4
4
Homework
Pg. 200 1 – 12 all, 14 – 40 E