Pr o b l em 4 Solving a Real-W orld Problem
Have you seen aPk,A s-
problem like this
before?
Yes, You wrote
the equation of a
perpendicular line in
Problem 3. Follow the
same steps here after
you calculate the slope of
the line from the graph.
Architecture An architect uses software to design
the ceiling of a room. The architect needs to enter an
equation that represents a new beam. The new beam
will be perpendicular to the existing beam, which is
represented by the red line. The new beam will pass
through the corner represented by the blue point.
What is an equation that represents the new beam?Step 1 Use th e slope form ula to find th e slope of the
red line th a t rep resen ts th e existing beam.m =_ 4 - 6 6 _ 3 Points (3,6) and (6, 4)are on the red line.Simplify.The slope of th e line th at rep resen ts th e
existing b ea m is — |.
Step 2 Find th e opposite reciprocal of th e slope
from Step 1. The opposite reciprocal of '3 1S 2-Step 3 Use point-slope form to write an equation. The
slope of th e line th a t rep resen ts th e new b ea m is
§. It will pass th rough (12,10). An eq u a tio n th at“ o
represents th e new b ea m is y - 10 = , (x ~ I2)q
or, in slope-intercept form, y = - 8.Got It? 4. W hat eq u a tio n could th e architect en ter to re p resen t a second b eam w hose
graph will p ass th rough th e corner at (0,10) a n d be parallel to th e existing
beam? Give your answ er in slope-intercept form.Lesso n Ch eck
you know HOW?
W hich equations below have graphs th a t are
parallel to one another? W hich have graphs th a t are
perpendicular to one another?
y = 6x y = 6x — 2
2.y = ~6*
W hat is an equation of th e line th a t passes through
(3, - 1 ) an d is parallel to y = -4x + 1? Give your
answer in slope-intercept form.MATHEMATICAL
Do yo u UN DERSTAND? PRACTICES- Vocabulary Tell w h e th e r th e two n u m b ers in each
p air are opposite reciprocals.
a. - 2 ,; c. 5, - 5 - Open-Ended Write equations of two parallel lines.
- C o m p a r e a n d C o n t r a s t How is determ ining if two
lines are parallel sim ilar to determ ining if they are
perpendicular? How are th e processes different? - W hat is an equation of th e line th a t passes through
(2, - 3 ) an d is p erp en d icu lar to y = x - 5? Give your
answ er in slope-intercept form.