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