Writing equations for lines that are parallel or coinciding to a given line.

1. Writing equations for lines that are parallel or coinciding to a given line.

2. Parallel Lines • Parallel lines have the same slope (m) and different y intercept (b). Example 1: y = 3x + 6 y = 3x - 7 What are the slopes of these lines? What are the slopes for any lines parallel to each other? m = 3/1 , b = 6 m = 3/1 , b = -7 The same

3. Coinciding Lines • Coinciding lines have the same(m) slope and same y-intercept (b). Example 2: y = 3x + 6 6y = 18x +36 Find m and b for each line. What do you notice about m and b? m = 3/1 , b = 6 m = 3/1 , b = 6 m and b are the same on both lines.

4. Parallel, Coinciding or Neither? 1) y = 4x + 2 2) y = 2x + 7 y = 4x - 2 y = 3x + 7 3) y = 5x + 2 4) y = 3x -6 2y = 10x + 4 y = 5 + 3x m = 4/1, m=4/1 parallel m = 2, m= 3 neither m = 5, m = 5 coinciding m = 3/1, m= 3/1 parallel

5. Step 1: Find the slope. Step 2. Substitute given x, y into the equation. Step 3: Solve for b. Step 4: Substitute m and b into the equation. Y = ___x + ___. m = 2 5 = 2 ( -1) + b 5 = -2 + b 7 = b Y = 2x + 7 Example 3: Write the equation of the line that is parallel to y = 2x + 3 and goes through the point (-1, 5)

6. Step 1: Find the slope. Step 2. Substitute given x,y into the equation. Step 3: Solve for b. Step 4: Substitute m and b into the equation. Y = ___x + ___. Example 4: Write the equation of the line that is parallel to 5y = -4x + 15 and goes through the point (-10, 2) m = -4/5 2 = -4/5 ( -10) + b 2 = 8 + b -6 = b Y = -4/5x -6

7. You try: • Write an equation that is parallel to y = 4x-5 thru the point (3,6). • Write an equation that is parallel to 3x - y = 7 thru the point (0,3) y = 4x - 6 y = 3x + 3