Linear Functions Worksheet Page 6
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38Section 1.1
Slopes and Equations of Lines
61
(c) Triangles M P Q; P N Q; and MN P are right
45. y = 4x + 5
triangles by construction. In triangles M P Q and
M N P;
Three ordered pairs that satisfy this equation are
(¡2; ¡3), (¡1; 1), and (0; 5). Plot these points
angle M = angle M;
and draw a line through them.
and in the right triangles P N Q and MN P;
angle N = angle N:
Since all right angles are equal, and since triangles
with two equal angles are similar, triangle M P Q
is similar to triangle M N P and triangle P NQ is
similar to triangle M NP:
Therefore, triangles M P Q and P N Q are similar
to each other.
(d) Since corresponding sides in similar triangles
are proportional,
46. y = ¡4x + 9
M Q = k ¢ P Q and P Q = k ¢ QN:
Three ordered pairs that satisfy this equation are
MQ
k ¢ P Q
(0; 9); (1; 5); and (2; 1): Plot these points and draw
=
P Q
k ¢ QN
a line through them.
MQ
P Q
=
P Q
QN
From the diagram, we know that P Q = 1:
1
M Q =
QN
From (a) and (b), m
= MQ and ¡m
= QN:
1
2
Substituting, we get
1
m
=
:
1
¡m
2
Multiplying both sides by m
; we have
2
47. y = ¡6x + 12
m
m
= ¡1:
1
2
Three ordered pairs that satisfy this equation are
44. y = x ¡ 1
(0; 12); (1; 6); and (2; 0): Plot these points and
draw a line through them.
Three ordered pairs that satisfy this equation are
(0; ¡1); (1; 0); and (4; 3): Plot these points and
draw a line through them.
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