Pregunta
6) What is the slope \( (m) \) of the line passing through the points \( (-8,5) \) and * point \( (-8,12) \) ? \( m=0 \) \( m= \) undefined \( m=-7 \)
Ask by Murray Hobbs. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The slope \( m \) is undefined.
Solución
To determine the slope \( m \) of the line passing through the points \( (-8, 5) \) and \( (-8, 12) \), we'll use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the given points:
\[
m = \frac{12 - 5}{-8 - (-8)} = \frac{7}{0}
\]
Dividing by zero is undefined in mathematics. Therefore, the slope \( m \) of the line is **undefined**.
**Answer:** \( m = \) undefined
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
When two points have the same x-coordinate but different y-coordinates, the line formed is vertical. In this case, both points \( (-8,5) \) and \( (-8,12) \) have an x-coordinate of \(-8\), making their line's slope undefined. A classic example can be seen in the city grid layout: vertical streets have no slope! When you calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), you can see why it leads to an undefined slope! Plugging in our points, we get \( m = \frac{12 - 5}{-8 - (-8)} = \frac{7}{0} \), and division by zero is a no-go in math!
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