5A Parallel and Perpendicular Lines
Parallel: Same slope
Perpendicular: -1/slope or the negative reciprocal
4 Step Process to finding the equation of the line
Step 0: Write coordinates (if necessary)
Step 1: Find the slope using the slope formula.
or by looking at the graph or if it is given or by getting equation into y=mx + b form
If it is parallel then use the same slope. If it is perpendicular then use -1/slope
Step 2: Using one of the points (x,y) and your slope, substitute into y=mx + b
Step 3: Solve for b
Step 4: Write the equation of the line in slope-intercept form.
Step 5: Verify with graph
Example 1: Write equation of a line that is parallel to the line y = 3/2x - 5 and goes through (-2,1)
Step 1: Slope is given as 3/2 since it’s y=mx + b form. Parallel slope is 3/2
Step 2: Using (-2,1) as (x,y), substitute m=3/2, x=-2, and y = 1 into y=mx + b
1 = 3/2 (-2) + b
Step 3: 1 = -3 + b
1 + 3 = b
4= b
Step 4: y = 3/2 x +4
Step 5: Verified by graphing J
Example 2: Write equation of the line that is perpendicular to the line 2x + y =6 and goes through (2,4)
Step 1: 2x + y = 6 à y = -2x + 6 so slope is -2. Perpendicular is -1/-2 à ½
Step 2: Using (2,4), substitute m=1/2, x = 2, and y = 4 into y=mx + b
4 = 2(1/2) + b
Step 3: 4 = 1 + b
3 = b
Step 4: y = 1/2x + 3
Step 5: Verify by graphing
Practice 1-5) Find the slope of the original line (a), the parallel line (b) and the perpendicular line (c)
1. y = -3x – 2 2. 3x + y = 8 3. x + 4y = 2 4. x = 3 5. Going through (-2, 3) and (5,2)
Orig: Orig: Orig: Orig: Orig:
Parallel: Parallel: Parallel: Parallel: Parallel
Perpendic: Perp: Perp Perp Perp
6-9) Write an equation of the line that is parallel to the graph of the given equation and passes through the given point.
6. , (1, 3) 7. , (2, 3) 8.. , (-3, 1) 9., (5, 6)
10. Determine if figure ABCD is a parallelogram with vertices: (-3, 4) (6, 4) (-5, -1) and (4, -1)
11. Determine if figure EFGH is a parallelogram if the vertices are : (0, 4) (-7, -3) (-2, -5) (4, -1)
12-15 Write an equation in slope intercept form of the line that is perpendicular to the graph of the given equation and passes through the given point.
12. , (-4, 2) 13.. , (0, 0)
14. , (3, 0) 15. , (2, -3)
16. Determine if the following is a rectangle:
(-3, -3) (0, -1) (2, -4) (-1, -6)
17. Determine if the following is a rectangle:
(1, -2) (2, 3) (-3, 5) (-2, -1)
18-20 Determine if the following are parallel, perpendicular, same line, or none of these.
18. 19. 20. 21.
22. Write the equation of the line that passes through the point (-1, -2) and is parallel to the graph of y = -3x – 2.
23. Write the equation of the line that passes through the point (4, -2) and is parallel to the graph of y = ½x – 7.
24. Write the equation of the line that passes through the point (-3, -2) and is perpendicular to the graph of x + 4y = 12.
25. Write the equation of the line perpendicular to the graph of y = -1/3x + 2 and passes through the x – intercept of that line.
26. Write the equation of the line that passes through the point (4, -1) and is perpendicular to the graph of y = 3.
27. Which line is perpendicular to 3x – 5y = 8 and goes through (5,-8)
A. 3x + 5y = 10 B. 5x + 3y = 12 C. 2x +y = 2 D. 10x + 6y= 2