Chapter 5-6: Geometry -Parallel and Perendicular Lines

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Write the slope-intercept form of an equation for the
line that passes through (4, –2) and is parallel to the
graph of
The line parallel to
Replace m with
point-slope form.
has the same slope,
and (x, y) with (4, -2) in the
Point-slope form
Replace m with
y with –2, and x with 4.
Simplify.
Distributive Property
Subtract 2 from each side.
Write the equation in slopeintercept form.
Answer: The equation is
Check
You can check your result by graphing both
equations. The lines appear to be parallel.
The graph of
passes through (4, –2).
Write the slope-intercept form of an equation for the
line that passes through (2, 3) and is parallel to the
graph of
Answer:
Geometry The height of a
trapezoid is measured on a
segment that is perpendicular
to a base. In trapezoid ARTP,
and
are bases. Can
be used to measure the
height of the trapezoid?
Explain.
Find the slope of each segment.
Slope of
Slope of
Slope of
Answer: The slope of
of
and
is 1 and the slope
is not perpendicular to
and
, so it cannot be used to measure height.
The graph shows the
diagonals of a rectangle.
Determine whether
is perpendicular to
Answer: The slope of
is
Since
is
and the slope of
is not perpendicular to
Write the slope-intercept form for an equation of a
line that passes through (4, –1) and is perpendicular
to the graph of
Step 1
Find the slope of the given line.
Original equation
Subtract 7x from
each side.
Simplify.
Divide each side
by –2.
Simplify.
Step 2
The slope of the given line is
So, the slope
of the line perpendicular to this line is the
opposite reciprocal of
or
Step 3
Use the point-slope form to find the equation.
Point-slope form
and
Simplify.
Distributive Property
Subtract 1 from
each side.
Simplify.
Answer: The equation of the line is
Check
You can check your result by graphing both
equations on a graphing calculator. Use the
CALC menu to verify that
passes through (4, –1).
Write the slope-intercept form for an equation of
a line that passes through (–3, 6) and is
perpendicular to the graph of
Answer:
Write the slope-intercept form for an equation of
a line perpendicular to the graph of
and passes through (0, 6).
Step 1
Find the slope of
Original equation
Subtract 5x from
each side.
Simplify.
Divide each
side by 2.
Simplify.
Step 2
The slope of the given line is
So, the slope
of the line perpendicular to this line is the
opposite reciprocal of
or
Step 3
Substitute the slope and the given point into the
point-slope form of a linear equation. Then write
the equation in slope-intercept form.
Point-slope form
Replace x1 with 0,
y1 with 6, and m with
Distributive Property
Answer: The equation of the line is
Write the slope-intercept form for an equation of
a line perpendicular to the graph of
and passes through the x-intercept of that line.
Answer:

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