Pregunta
Find the slope of a line perpendicular to the line whose equation is
. Fully
simplify your answer.
simplify your answer.
Ask by Colon Warner. in the United States
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The slope of a line perpendicular to
is -2.
Solución
To find the slope of a line perpendicular to the given line
, follow these steps:
-
Rearrange the Equation to Slope-Intercept Form (
): Start with the given equation:Solve for: So, the slope () of the given line is . -
Determine the Slope of the Perpendicular Line:Perpendicular lines have slopes that are negative reciprocals of each other. This means if the slope of one line is
, the slope of a perpendicular line is . Given the slope, the slope of the perpendicular line ( ) is: -
Final Answer:The slope of a line perpendicular to the given line is
.
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Como
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Extra Insights
To find the slope of a line perpendicular to the given line, we first need to determine the slope of the original line from its equation
. We can rewrite this in slope-intercept form (y = mx + b).
- Rearranging the equation:
From this, we can see that the slope (m) of the original line is
.
- The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
Therefore, the slope of the perpendicular line is:
Finally, the slope of the line perpendicular to the given line is
.
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