#### Transcript 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.
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
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
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
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
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
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.