Parallel Lines Introduction What are parallel lines Lines

Parallel Lines

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

Now that we know what parallel lines are, let’s go back to line equations… 7 6 5 (3, 4) 4 3 (2, 2) 2 1 0 -4 -3 -2 -1 -1 0 1 2 3 4 -2 -3 What is the equation of the pink line? y = ax+b 4 = 2(3)+b 4=6+b 4 -6 = b -2 = b y = 2 x -2

Now let’s find the equation of the second line! 7 (1, 6) 6 5 (3, 4) 4 3 (2, 2) 2 1 (-2, 0) -4 -3 -2 0 -1 -1 0 1 -2 -3 y = 2 x + 4 2 3 4

Let’s sum up what we’ve done so far… 7 (1, 6) 6 5 (3, 4) 4 3 (2, 2) 2 1 (-2, 0) -4 -3 -2 0 -1 -1 0 1 -2 -3 y = 2 x -2 What do you notice? y = 2 x + 4 à The lines are parallel à The slopes are the same 2 3 4

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

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

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

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

Find an equation that contains (-4, 3) and is parallel to: 6 Write the new equation and plug in the given coordinate to isolate “b” (0, 5) 5 4 3 (1, 2) 2 1 0 -4 -2 0 2 4 y = -3 x + b 3 = -3(-4) + b 3 = 12 + b 3 - 12 = b -9 = b y = -3 x – 9