1. Notes: Lesson 5-6 A Objective: Write an equation for a line through a given point that is parallel to a given line. Lines that don’t touch because they have the same slope.

2. Example: Before we do this example, let’s graph y = ½ x – 1 and include the point (4, -2) on the graph.

3. Example: Find the equation of the line that is parallel to the given line y = ½ x -1 but that goes through the point (4, -2) What is the equation of this line?

4. 4 Steps: 1. Change the equation to slope-intercept form (y = mx +b). 2. Identify the slope 3. Write the new equation using the slope and given point. 4. Change to slope intercept form (solve for y). Given: y = ½ x - 1 m = 1/2 y – y 1 = m ( x – x 1 ) point-slope form is easy! y – (-2) = ½ ( x – 4) y + 2 = ½ x - 2 y = ½ x - 4 * already y = mx + b : ) ll m = 1/2

5. Try this: Find the equation of the line parallel to -3x + y = 4 that goes through the point (-2, 2). 1. slope intercept form (y = mx + b) y = 3x + 4 2. Identify m m = 3 ll m = 3 3. Write the new equation y – y 1 = m ( x – x 1 ) y – 2 = 3 ( x – (-2)) 4. Change to slope intercept form. y - 2 = 3 (x +2) y = 3x + 8 -3x + y = 4 +3x = +3x

6. Did you master today’s objective? Of course you did!!! Show your stuff with this last example:

7. Try this: Find the equation of the line parallel to y = 2x – 1 that goes through the point (1, -3). 1. slope intercept form (y = mx +b)y = 2x - 1 2. Identify mm = 2 ll m = 2 3. Write the new equation y – y 1 = m ( x – x 1 ) y – (-3) = 2 ( x – 1) 4. Change to slope intercept form. y + 3 = 2x - 2 y = 2x - 5

8. Lesson 5-6A, page 296 #14-24 evens Work must be shown! Leave answers in y = mx+b form! Assignment: