Answers and Explanations 151
Answers
1–100
64.
y = 4x + 5
The graph of y = mx + b is a line with slope of m and a y-intercept at (0, b). Therefore,
using m = 4 and b = 5 gives you the equation y = 4x + 5.
65.
y
x
=
+
5
6
14
3
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 (–2, 3) and (4, 8) is
m
y y
x x
=
−
−
=
−
− −
=
2
1
2
1
8 3
4
2
5
6
( )
Now use the slope and the point (4, 8) in the point-slope formula:
y y m x x
y
x
y
x
y
x
y
x
− =
−
− =
−
− =
−
=
−
+
=
−
+
1
1
8 5
6
4
8 5
6
20
6
5
6
10
3
8
1
5
6
10
3
24
(
)
(
)
3 3
5
6
14
3
y
x
=
+
66.
y
x
=
+
3
4
17
4
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 two lines are parallel, so the slopes are the same. Therefore, the slope of the line
you’re trying to find is m = 3
4
.
Using the slope and the point (1, 5) in the point-slope formula gives you
y y m x x
y
x
y
x
y
x
y
x
y
− =
−
− =
−
− =
−
=
− +
=
− +
=
1
1
5 3
4
1
5 3
4
3
4
3
4
3
4
5
1
3
4
3
4
20
4
(
)
(
)
3 3
4
17
4
x +