Avani wrote the linear equation y = 5 x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5 x + 4 and that passes through (15,–2). If her new equation is in the form y = negative one-fifth x + b, what is the value of b?
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Answer:
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Step-by-step explanation:
Point-slope form:
y
−
7
=
7
15
(
x
+
1
)
Slope-intercept form:
y
=
7
15
x
+
112
15
Explanation:
The slope of a perpendicular line is the negative reciprocal of the original slope. In this case, the perpendicular slope of
−
15
7
is
7
15
. The product of two perpendicular slopes is
−
1
.
−
15
7
×
7
15
=
−
1
With the slope and one point, you can write a linear equation in point-slope form:
y
−
y
1
=
m
(
x
−
x
1
)
,
where:
m
is the slope, and
(
x
1
,
y
1
)
is the given point.
Plug in the known values.
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