1. Parallel Lines

2. Introduction What are parallel lines?
 Lines that never touch, never intersect
Which graphs represent two paralell lines?

3. Now that we know what parallel lines are, let’s go back to line equations…
(3,4)
(2,2)
What is the equation of the pink line?
y = ax+b
4 = 2(3)+b 4 = 6 + b 4-6 = b
-2 = b
y = 2x -2
a = 𝑦2−𝑦1 𝑥2−𝑥1 = 4−2 3−2 =2

4. y = 2x + 4 Now let’s find the equation of the second line! (1,6) (3,4)
(2,2)
(1,6)
(-2,0)
y = 2x + 4

5. y = 2x -2 y = 2x + 4 Let’s sum up what we’ve done so far…
(3,4)
(2,2)
(1,6)
(-2,0)
y = 2x -2
What do you notice?
The lines are parallel
The slopes are the same
y = 2x + 4

6. Two PARALLEL lines have the SAME SLOPE !
WAIT, WHAT?
Two PARALLEL lines have the SAME SLOPE !

7. Which of the following are parallel?
Exercise
Which of the following are parallel?
y = 2x – 1
y = -3x +7
y = 2x + 5
y = 4x – 3
y = -3x – 3
y = 4x + 5
a) & c)
b) & e)
d) & f)

8. Step 3: Write new equation
How to find the equation for the line that contains (5,1) and is parallel y = 5x – 4.
Step 1: Write the slope
y = 5x – 4
a = 5
Step 3: Write new equation
y = 5x – 24
Step 2: Write the new equation and plug in the given coordinate to isolate “b”
y = 5x + b
1 = 5(5) + b
1 = 25 + b
1 – 25 = b
-24 = b
y = 5x – 24

9. Find the equation for the line that contains (2,-6) and is parallel y = 3x + 9.

10. y = -3x – 9 Find an equation that contains (-4,3) and is parallel to:
(0,5)
Write the new equation and plug in the given coordinate to isolate “b”
y = -3x + b
3 = -3(-4) + b
3 = 12 + b
= b
-9 = b
(1,2)
Extra step! Find the slope of the first equation.
a = 𝑦2−𝑦1 𝑥2−𝑥1 = 2−5 1−0 =−𝟑
y = -3x – 9