66: Parallel and Perpendicular Lines

1
6-6 Parallel and Perpendicular Lines
OBJECTIVES You will be able to determine if two
lines are parallel or perpendicular by their
slopes, and write equations of lines that pass
through a given point, parallel or perpendicular
to the graph of a given equation.

• This section introduces two new ways to hide
  the slope you need to graph a linear equation.
• You will still use the point-slope and slope
  formulae.
• Terms to memorize
• parallel lines - two lines which do no intersect
• Parallel lines have identical slope. Memorize
  this fact.
• perpendicular lines - two lines which intersect
  at a ninety-degree angle
• Perpendicular lines have negative reciprocal
  slopes. Memorize this fact.

2
6-6 Parallel and Perpendicular Lines
These lines are parallel.
Parallel lines never cross.
Perpendicular lines form four 90 angles.
3
6-6 Parallel and Perpendicular Lines
EXAMPLE 1 Write an equation in slope-intercept
form of the line that passes through (4, 0) and
is parallel to the graph of 4x - 3y 2.
Remember, to find equations of lines, we must
know two things (1) the slope, and (2) a
point. Do we know a point of this line? Yes, (4,
0) Do we know the slope? not directly slope is
hidden Since the line we are looking for is
parallel to the line given in the problem, we can
find the slope of the given line and it will be
identical to the slope of the line we are trying
to find. To find the slope of 4x - 3y 2, get
it in slope-intercept form.
4x - 3y 2
y - y1 m(x - x1)
- 3y -4x 2
Now we have the slope and a point. Use the
point-slope formula.
Finally, the problem asked that the answer be in
slope-intercept form. So solve the new equation
for y.
4
6-6 Parallel and Perpendicular Lines
EXAMPLE 2 Write the slope-intercept form of an
equation that passes through (8, -2) and is
perpendicular to the graph of 5x - 3y 7.
Remember, to find equations of lines, we must
know two things (1) the slope, and (2) a
point. Do we know a point of this line? Yes, (8,
-2) Do we know the slope? not directly slope is
hidden Since the line we are looking for is
perpendicular to the line in the problem, we can
find the slope of that line and it will be the
negative reciprocal of the slope of the line we
are trying to find. To find the slope of 5x - 3y
7, get it in slope-intercept form.
5x - 3y 7
Now we have the slope and a point. Use the
point-slope formula.
Finally, the problem asked that the answer be in
slope-intercept form. So solve the new equation
for y.
- 3y -5x 7
y - y1 m(x - x1)
We are looking for a line perpendicular to the
one given in the problem. The slope of the line
in the problem is 5/3. Since we are looking for
perpendicular lines, the slopes are negative
reciprocals of each other. So, the slope of the
new line will be -3/5.
5
6-6 Parallel and Perpendicular Lines
HOMEWORK
Page 367 21 - 39 odd