Warm Up Identify the slope and yintercept 1

Warm Up Identify the slope and y-intercept 1. -3 x + 5 y = 9 Graph the equation. 2. -2 x + 4 y = 8 3. 2 x + 7 y = 7

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Warm Up Answers Continued

Lesson 7. 1 A Writing equations for lines that are parallel or coinciding to a given line.

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

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

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

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

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

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

Summary: • What is the difference between parallel lines and coinciding lines when writing equations? Homework Worksheet 7. 1 A