Parallel and Perpendicular Lines

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Parallel Lines• Parallel lines do not intersect!

y = 2x + 4 and y = 2x + 3 will be parallel.

• Parallel lines will have the same slope and different y-intercepts.

Parallel Lines

y = 2x + 4 and y = 2x + 3 will be parallel.

Parallel Lines• Write the slope-intercept form of an

equation for the line that passes through (-1,-2) and is parallel to the graph of y = -3x -2. THE SLOPE OF BOTH EQUATIONS WILL BE -3.

y = mx + b (-1,2) SLOPE = -3 -2 = -3(-1) + b -2 = 3 + b -3 = -3 - 5 = b The equation is: y = -3x -5

• Example 2Write the slope-intercept form

of an equation for the line that passes through (4,-2) and is parallel to the graph of y = 1 x -7

2( The slope will be 1 ) 2

Parallel Lines• Write an equation of the line

containing the point (0,6) and parallel to the line: The slope will be -3

y = -3x + 4

Perpendicular Lines

• Perpendicular lines intersect and form rt. angles. The product of the slopes is -1.

• Ex if a slope is -3, then the other slope of the line is 1

3 BECAUSE:

-3 * 1 = -1

1 3

Perpendicular Lines• If a slope is -1 the line perpendicular

4

to that line must be 4 because:

-1 * 4 = -4 = -1

4 1 4

Perpendicular Lines• Write the slope-intercept form of an equation

that passes through (-2, 0) and is

perpendicular to the graph of y = x -6

Slope of equation is 1, New slope must be

-1 because 1 * -1 = -1

1 1

y = x -6

0 = -1(-2) + b

0 = 2 + b

b = -2

Equation: y = -1x – 2 or y = -x -2

Perpendicular Lines

• Write the slope-intercept form for an equation for the line that passes through

(-1,3) and is perpendicular to 2x + 4y = 12

a) Solve for y in terms of x: 2x + 4y = 12

b) Substitute values in for x, y, and m

Practice• Write the slope-intercept form of an equation

of the line that passes through the given point and is ll to the graph of the equation.

1) (3,2), y = 3x + 4 2) (-1,-2) y = -3x + 5

Practice

• Write the slope-intercept form of an equation of the line that passes through the given point and is ll to the graph of the equation.

3) (3,2), y = 3x + 4 4) (-5,-1), 2y = 2x -4

Practice• Write the slope-intercept form of an equation of

the line that passes through the given point and is perpd.( l ) to the graph of each equation.

5) (-3,-2), y = x + 2 6) (4,-1), y = 2x -4

Practice• Write the slope-intercept form of an equation

of the line that passes through the given point and is l to the graph of each equation.

7) (-5,1), y = - 5 x -7 8) (-2,2) 6x + 3y = -9

3

Guided Practice• See pg 295 #4