Part II: The Answers
152
Answers
1–100
67.
y
x
=
−
3
2
17
2
The equation of a line that goes through the point (x 1 , y 1 ) and has a slope of m is given
by the point-slope formula: y – y 1 = m(x – x 1 ).
The slope of the line that goes through the points (–6, 2) and (3, –4) is
m
y y
x x
=
−
−
= − −
− −
= − = −
2
1
2
1
4 2
3
6
6
9
2
3
( )
The slopes of perpendicular lines are opposite reciprocals of each other, so the slope
of the line you want to find is m = 3
2
(you flip the fraction and change the sign).
Using the slope and the point (3, –4) in the point-slope formula gives you
y y m x x
y
x
y
x
y
x
y
x
− =
−
− − =
−
+ =
−
=
− −
=
− −
1
1
4
3
2
3
4 3
2
3
3
2
9
2
4
1
3
2
9
2
8
(
)
( )
(
)
(
)
2 2
3
2
17
2
y
x
=
−
Here’s what the perpendicular lines look like:
68.
y
x
=
− +
2
3 4
Stretching the graph of y
x
=
vertically by a factor of 2 produces the equation y
x
= 2 .
To shift the graph of y
x
= 2
to the right 3 units, replace x with (x – 3) to get
y
x
=
−
2
3. Last, to move the graph of y
x
=
−
2
3 up 4 units, add 4 to the right side to
get y
x
=
− +
2
3 4.