13.2 EQUATIONS OF A
LINE
Neha Pancholy Period 9
Slope-Intercept Form/Y-Form

The y-form
or slope intercept form
of a non vertical line is
y= mx + b
 m= slope
 b= y-intercept
Using y-form to Graph Lines




Ex. y=2x + 1
Begin by plotting the yintercept
Count up/down the
number of points of the
rise and right/left for
the run
For any 2 points on a
line, the rise divided by
the run equals the
SLOPE
Standard Form
ax + by = c
a, b, c are real, whole numbers
The a coefficient is always positive!!!
More Equations

For a horizontal line:

For a vertical line:
y= b
x= a
is the y coordinate
of every point on the
line
a is the x coordinate of
every point on the line
b
Sample Problems
Identify the Equation of the Lines on the
Graphs
Ex.
Horizontal line
Slope (m)= 0
Y-intercept= 2
y = mx + b
Answer: y = 0x + 2
y= 2
Ex.
x intercept= (4, 0)
y intercept= (0,1)
Find slope: 1  0 
04
1
4
Answer: y=1/-4x+1
Point Slope Form

This is a way to write an equation using the slope
and a point on the line.


y-y1 = m(x-x1)
Ex. A line containing (1,8) with the slope of 4.
 y-8
= 4(x-1)
Practice Problems (Point-Slope)



Find the equation of a line with a slope of ¼
containing the point (-2,3).
Find the equation of a line with the slope of 2 and
containing the point (5,1)
Find the equation of a line perpendicular to a with
a slope of -3/2 containing (-2,3)
Answers to “Practice Problems PointSlope”



y-3 = ¼ (x+2)
y-1 = 2(x-5)
y-3 = -3/2(x+2)
Equations of Lines Extended
Ex.Given: A = (-3,2) B= (5, -6) and C= (-7, 10)
1. Find the equation of the median
of
drawn
ABCfrom point A to
1. Find the midpt.
BCof
5  7  6  10
BC
M BCthe
 slope, using the
 (midpt.
1,2)
2. Find
2
2
and the point from which the
median will be drawn.
22
 0is a horizontal
3. In this case, the line
1 2
line, so simply set y equal to the
y-coordinate of both ordered
pairs.
Answer: y=2
Equations of Lines Practice Problems
2
1.



Given: D= (4,5), E=(2,4),
C= (6,8)
Find the equation of
the altitude drawn
from E to DC
Write the final answer
in standard form.


.
Find the equation of a
line parallel to
y=4x+1, containing
the point (2,6).
Write final answer in
standard form.
More Practice Problems
3. Which of the following
equations passes through the
points (2,1) and (5,-2)?


Choose:
A. y = (3/7)x + 5
B. y = -x + 3
C. y = -x+2
D. y = (-1/3)x + 3
4. Does the graph of the straight
line with slope of -2 and yintercept of -3 pass through the
point (5,-13)?
5. What is the slope of the line 3x +
2y = 12?
6. Does the line 2y + x = 7 pass
through the point (1,3)?
Practice Problems (cont’d)
7. x-intercept of 3 and a
y-intercept of 12
Express in standard form
8. Show that
3x + 2y = 22
and
y- 5 = -3/2(x-4)
are equivalent.
Answers to “Equations of Lines Practice
Problems”
1.
mDC =
85
64
m   2 3
y-4 = -2/3(x-2)
y-4 = -2/3x + 4/3
3y-12 = -2x +4
Answer: 2x+3y = 16
2. Parallel to y=4x+1,
so m = 4
y-6 = 4(x-6)
y-6 = 4x – 24
4x – y = -18
Answers to “More Practice
Problems”
 2 1
52
3. m=
y-1 = -1(x-2)
y-1 = -x + 2
y = -x + 3
Answer: B
4. y = -2x-3
(-13) ? -2(5)-3
-13 = -13
Answer: yes
5. 3x + 2y = 12
2y = -3x + 12
y = -3/2x + 6
Answer: m = -3/2
6. 2y + x = 7
2(3) + 1 ? 7
6+1 ? 7
7=7
Answer: Yes!
Answers to “Practice Problems
(cont’d)”
7. m= 12  0  12  4 8. 3x + 2y =22
03 3
2y= -3x +22
y= -3/2x + 11
y-12 = -4(x-0)
y-12 = -4x
Answer: 4x+y = 12
y-5 = -3/2(x-4)
y-5 = -3/2x +6
y = -3/2x+ 11
Works Cited
"Determining the Equation of a Line From a Graph". algebra.help. 29 May
2008 <http://www.algebrahelp.com
/worksheets/view/graphing/eqfromgraph.quiz>.
Oswego City School District, "Practice With Equations of Lines". Regents. 28
May 2008 <http://www.regentsprep.org
/Regents/Math/glines/PracLine.htm>.
"Slope". Barnes and Noble. 29 May 2008
<http://www.sparknotes.com/math/algebra1/graphingequations/section4.
rhtml>.