7.8 Parallel and Perpendicular Goals: To identify parallel, perpendicular lines and write an equation of a line containing a point and parallel or perpendicular to a line

“parallel”

Slope and Line relationships Parallel lines have the same exact slope (“m”) and a different y-intercept (“b”). y = 2x +3 and y = 2x +11 are parallel. All vertical lines are parallel. x = -5 and x = 9 are parallel. To determine if two equations are parallel, change the equation to its slope intercept form ( y = mx + b )

Determine if the lines are parallel Y

Y

N Must have different y-intercept

Determine if the lines are parallel N

Y All vertical lines are parallel.

Determine if the lines are parallel N

Y

N

Y

Perpendicular means “at right angles” All three red lines are perpendicular to the green line.

Slope and Line relationships Parallel lines have the same exact slope (“m”) and a different y-intercept (“b”). y = 2x +3 and y = 2x +11 are parallel. Perpendicular lines (  ): have the opposite reciprocal slopes y = 2x + 3 and y = are perpendicular.

Determine if the lines are perpendicular: Y

N One must be positive; the other negative.

Determine if the lines are perpendicular: Y

Y

Y

Y

Write an equation of a line given a point and perpendicular to the line Given: (0,6) and y-3x =4 1.) Find slope: Solve for y, y=3x + 4 m= 3 2.) Take the Perpendicular to the slope m=-1/3 3.) Use your m and your point and plug it into a new y=mx+b m=-1/3 (0,6) 6=-1/3 (0) + b 4.) solve for b, 6 =b 5.) write your equation with m and b y=-1/3x +6

Write an equation of the line containing the given point and parallel to the line (0,2) 3y-x =0 -Solve for y to find the slope y=1/3 x -A slope parallel to m =1/3 would be m=1/3 - Use your slope and ordered pair to solve for b (0,2) m =1/3 2=1/3(0) +b 2=b and m=1/3 4. Write the equation with m and b Y=1/3x +2

Assignment: Page 340 (2-30) even Show solving for “y”

3 Corners Go to the: 1.) parallel, 2.) perpendicular 3.)neither corner You may want a pencil and paper

Determine if the lines are parallel (1), perpendicular (2), or neither (3) 1

1

3 Must have different y-intercept

Determine if the lines are parallel (1), perpendicular (2), or neither (3) 3 Product of slopes must be negative 1

Determine if the lines are parallel (1), perpendicular (2), or neither (3) 1 All vertical lines are parallel.

Determine if the lines are parallel (1), perpendicular (2), or neither (3) 2

2

3

1