Transcript Day Problems • Graph each equation. 1. y – 2 = (x – 3) 2.

Day Problems
• Graph each equation.
1. y – 2 = (x – 3)
2. y + 3 = -2(x – 1)
• Write an equation in point-slope form for the
line through the given point with the given
slope.
3. (4 , 2); m = 3
4. (-5 , 2); m = 0
• A line passes through the given points. Write an equation
for the line in point-slope form. Then rewrite the equation
in slope-intercept form.
5. (-1 , 0) , (1 , 2)
6.5 Parallel and Perpendicular Lines 2/22/11
• Parallel lines – lines in the same plane that
never intersect.
Slopes of Parallel Lines
• Nonvertical lines are parallel if they have the
SAME SLOPE and DIFFERENT
Y-INTERCEPTS. Any two vertical lines are
parallel.
• Example – The equations y = 2x + 1 and
y = 2x + 3 have the same slope, 2, and different
y-intercepts. The graphs of the two equations
are parallel.
Determining Whether Lines are Parallel
1
y   x  5 and 2x + 6y = 12
3
• Are the graphs of
parallel? Explain.
• Write 2x + 6y = 12 in slope-intercept form. Then
1
compare with y   x  5.
3
6 y  2 x  12
6 y 2 x  12

6
6
1
y  x2
3
• The lines are parallel. The equations have the same
slope,  1 , and different y-intercepts.
3
Writing Equations of Parallel Lines
• Write an equation for the line that contains (5 , 1) and
is parallel to y  3 x  4.
5
• Step 1 – Identify the slope of the given line.
3
m
5
• Step 2 – Write an equation of the line through (5 , 1)
using point-slope form, then change to slope3
intercept.
y  y1  m( x  x1 ) y  1  x  3
3
y  1  ( x  5)
5
3
3
y  1  x  (5)
5
5
5
3
y  x2
5
Perpendicular Lines
2/23/11
• Perpendicular lines – lines that intersect to form
right angles.
• SLOPES OF PERPENDICULAR LINES
– Two lines are perpendicular their slope is the
opposite reciprocal of the given slope. A vertical
and horizontal line are also perpendicular.
1
y   x 1
4
• EXAMPLE – the slope of
is 1 The slope of y = 4x + 2 is 4.
 .
4
Opposite Reciprocal
• How to find the opposite reciprocal of a number:
5
Start with 3 Find its
 .
 .
3
a fraction 5 reciprocal
Start with
an integer
4.
Find its
reciprocal
1
.
4
Write the
opp. reciprocal
5
.
3
Write its
opp. reciprocal
1
 .
4
Writing Equations for Perpendicular Lines
• Find an equation of the line that contains (0 , -2) and
is perpendicular to y = 5x + 3.
• Step 1- Identify the slope of the given line.
m=5
• Step 2 – Find the opposite reciprocal of the slope:
1

5
• Step 3 – Use the slope-intercept form to write an
equation.
y  mx  b
1
y   x  ( 2)
5
1
y   x2
5
More Practice!!!
• Textbook – p. 314 #2 – 30 even.
• Homework – Worksheet 6.5.