Pregunta
If a line has a slope of
, what is the slope of a line that is perpendicular to it?
Ask by Johnson Graham. in Lesotho
Jan 18,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The slope of the perpendicular line is
.
Solución
To find the slope of a line that is perpendicular to another line, we use the property that the slopes of two perpendicular lines are negative reciprocals of each other.
Given that the slope of the original line is
, the slope of the line that is perpendicular to it, denoted as
, can be calculated using the formula:
Substituting the value of
:
Thus, the slope of the line that is perpendicular to the line with a slope of
is
.
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Como
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Extra Insights
To find the slope of a line that is perpendicular to another line, you take the negative reciprocal of the original line’s slope. A slope of
means the perpendicular slope would be
. This is because the negative reciprocal of
(where
is the slope) is
. So, if you flip
, you get
, but we need to apply the negative, resulting in a positive value:
.
Now you’ve got your
slope, ready to rock! You can visualize these lines: one might slant steeply downwards, while the other gently rises upwards, making for a perfect high-five at their intersection!

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