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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.

6-6 Parallel and Perpendicular Lines

These lines are parallel.

Parallel lines never cross.

Perpendicular lines form four 90 angles.

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.

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.

6-6 Parallel and Perpendicular Lines

HOMEWORK

Page 367 21 - 39 odd

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