2.  Must write the equation in the
form Ax+By=C
 Find 2 points on the line whose
coordinates are both integers
 Use the values of the coordinates
to fine the slope of the line using
the formula m=y2-y1/x2-x1

3.  Use values found for slope and a
coordinates
 Then write it in point-slope form y-
y1=m(x-x1)
 Solve for y

4.  Example:
 M= 5, (6,3)
 Y-3=5(x-6) Write equation
 Y-3=5x-30 Distribute the 5
 Y=5x-27 Add 3 to both sides

5.  Then to make it into standard form
we may need to add or subtract
from either side
 Example:
 Y=5x-27 Add 27 to both sides
 Y+27=5x Subtract y from both
sides
 27=5x-y
 This is in Standard Form

6.  Point-slopeform
y-y1=m(x-x1)
 Standard Form
Ax+By=C
 Slope formula
m=y2-y1/x2-x1

7.  An equation of the line with slope
m and y-intercept
 To find y-intercept, find where the
point crosses the y-axis or where
x=0
 It’s the y-intercept of that point Ex:
(0,5) so the intercept is 5

8.  Then use slope formula m=y2-
y1/x2-x1
 Use the point that you found for
the y-intercept
 Then find another point whose
coordinates are integers

9.  Once you have found the y-
intercept
 Also once found the slope
 Plug each one into the formula
y=mx+b in the correct places

10.  Example:
Given points (0,6) (3,12)
Find the slope and the y-intercept
M=12-6/3-0=6/3=2
Plug into y=mx+b

11.  Use the point that crosses the y-
axis
 M=2, y-intercept=6
y=2x+6
 Remark: positive slope rises left to
right, negative slope falls left to
right

12.  To find a line perpendicular to
another
 First we need to know the slope of
the first line
 Perpendicular lines have the
opposite reciprocal of the normal
line

13.  Once found the slope of the
perpendicular line
 Use the point slope equation to
find the equation of that line
 Then solve for y and put in slope
intercept form

14.  Example:
Given two points (5,10)
(8,16)
 Find the equation of the normal
and perpendicular
 First: Find the slope of the normal
line

15.  M=16-10/8-5=6/3=2
 Plug into point slope to find equation
of the normal line, pick either point
 M=2 (5,10)
y-10=2(x-5)
y-10=2x-10
y=2x

16.  Now find the perpendicular line
 The slope is opposite and the
reciprocal of the normal
 M=-1/2, then just pick a point
again and plug it into point slope
formula

17.  M=-1/2, (5,10)
 Y-10=-1/2(x-5)
 Y-10=-1/2x+5/2
 Y=-1/2x+25/2
 Now we have both equations