Edited by Alex
If lines are parallel the SLOPES ARE THE SAME!!!
Steps
 Get each equation in y = mx + b (slope intercept format)
 Look at the slope (m) for each line
 If they are the same then they are PARALLEL
If lines are perpendicular the slopes are the NEGATIVE RECIPROCAL.
Steps
 Get each equation in y = mx + b (slope intercept format)
 Look at the slope (m) for each line
 If the slopes are the same they are parallel, not perpendicular.
 If both slopes are positive or both slopes are negative then the lines are NOT perpendicular, you should have one of each.
 Make sure that the slopes are FLIPPED (Reciprocal )
 If the slopes are flipped and one positive and one negative, then the lines are perpendicular.
Examples:
Equation 
Parallel Equation Sample 
Perpendicular Equation Sample 
y = 3x  2 
y = 3x + 5 
y = 1/3x  75 
y = 1/5x + 9 
y = 1/5x + 43 
y = 5x + 12 
y = 2/3x  6 
y = 2/3x + 56 
y = 3/2x  19 






y=mx+b
2x+y=1
4y=2x8
You want to always get your equations in y=mx + b (slope intercept) format. Or as I say.. y alone in his home.
y=2x+1
y=1/2x2
The slopes are 2 and 1/2 so the lines are perpendicular
1. Determine if the lines 6x3y=12 and 10x+5y=20 are parallel or perpendicular
6x3y=12 Needs to be in y = mx + b format, get y alone in his home.
3y=6x+12
y=2x4
10x+5y=20 Needs to be in y = mx + b format, get y alone in his home.
5y=10x20
y=2x4
The slope of the first line is 2 and the slope of the 2nd line 2, this is a Common TRICK! These lines are NEITHER.
They are not parallel, the slopes are NOT the same
They are NOT perpendicular, the slopes are NOT flipped over.
However, the y intercepts are the same, just saying.
3. Determine if the lines y=3x+1 and 3x+y=2 are parallel or perpendicular
The first line: y=3x+1 is already in slope intercept form.
3x+y=2 Needs to be in slope intercept form.
3x 3x
y=3x+2
The slope of the first line is 3 and the slope of the 2nd line is 3, so the lines are PARALLEL. They have the same slope.
4. Write the equation of the line that contains (1,6) and is parallel to the line y=4x+5
slope is 4
y6=4(x1)
START by putting the slope from the first line into y  y_{1} = m(x  x_{1}) point slope form. Then fill in the
5. Write the equation of the line that contains (2,10) and is perpendicular to the line y=2x+4
perp slope =1/2
y10 =1/2x+1 Plug in the PERPENDICULAR SLOPE into the point slope form equation, then solve for y (that means distribute and add the 10 to both sides)
y=1/2x+11
Notice on the graph that there are TWO lines. Sometimes students forget that we are talking about two lines. The lines are perpendicular.
6.
2x5y=10
2x 2x
5y=2x+10
y=2/5x2 Wanted to solve for y, get into y = mx + b so you can see that the slope is 2/5 and the y intercept is 2
7.
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