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
Use values found for slope and a
coordinates
Then write it in point-slope form y-
y1=m(x-x1)
Solve for y
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
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
Point-slope form
y-y1=m(x-x1)
Standard Form
Ax+By=C
Slope formula
m=y2-y1/x2-x1
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
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
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
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
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
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
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
Example:
Given two points (5,10)
(8,16)
Find the equation of the normal
and perpendicular
First: Find the slope of the normal
line
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
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
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