Question
Given the graph, select the equation that is perpendicular
a
y=(5/6)x+5
b
y=(-6/5)x-5
c
y=(-1/3)x-4
a
y=(5/6)x+5
b
y=(-6/5)x-5
c
y=(-1/3)x-4
Answers
GPT-4o mini
To find an equation that is perpendicular to a given line, we need to look for a line whose slope is the negative reciprocal of the slope of the original line.
Assuming you have a specific line, you'll calculate its slope and then find the negative reciprocal. However, since you haven't provided the slope of the original line, I will explain how to determine the perpendicular slope using the options given.
1. **Identify the slope of the given line**. The slope-intercept form of a line is **y = mx + b**, where **m** is the slope.
For the options you provided:
a. \( y = \frac{5}{6}x + 5 \) → slope \( m = \frac{5}{6} \)
b. \( y = -\frac{6}{5}x - 5 \) → slope \( m = -\frac{6}{5} \)
c. \( y = -\frac{1}{3}x - 4 \) → slope \( m = -\frac{1}{3} \)
2. **Find the negative reciprocal** of each slope:
- For option (a) \( \frac{5}{6} \): The negative reciprocal would be \( -\frac{6}{5} \).
- For option (b) \( -\frac{6}{5} \): The negative reciprocal would be \( \frac{5}{6} \).
- For option (c) \( -\frac{1}{3} \): The negative reciprocal would be \( 3 \).
From this analysis, we can see that:
- **Option (b)** \( y = -\frac{6}{5}x - 5 \) is perpendicular to the original line with slope \( \frac{5}{6} \), as it has the opposite sign and the reciprocal slope.
Therefore, if the original line has a slope of \( \frac{5}{6} \), the correct answer for the perpendicular line is **option (b)**: \( y = -\frac{6}{5}x - 5 \). If you have a different line whose slope you want to test against, follow the same method!
Assuming you have a specific line, you'll calculate its slope and then find the negative reciprocal. However, since you haven't provided the slope of the original line, I will explain how to determine the perpendicular slope using the options given.
1. **Identify the slope of the given line**. The slope-intercept form of a line is **y = mx + b**, where **m** is the slope.
For the options you provided:
a. \( y = \frac{5}{6}x + 5 \) → slope \( m = \frac{5}{6} \)
b. \( y = -\frac{6}{5}x - 5 \) → slope \( m = -\frac{6}{5} \)
c. \( y = -\frac{1}{3}x - 4 \) → slope \( m = -\frac{1}{3} \)
2. **Find the negative reciprocal** of each slope:
- For option (a) \( \frac{5}{6} \): The negative reciprocal would be \( -\frac{6}{5} \).
- For option (b) \( -\frac{6}{5} \): The negative reciprocal would be \( \frac{5}{6} \).
- For option (c) \( -\frac{1}{3} \): The negative reciprocal would be \( 3 \).
From this analysis, we can see that:
- **Option (b)** \( y = -\frac{6}{5}x - 5 \) is perpendicular to the original line with slope \( \frac{5}{6} \), as it has the opposite sign and the reciprocal slope.
Therefore, if the original line has a slope of \( \frac{5}{6} \), the correct answer for the perpendicular line is **option (b)**: \( y = -\frac{6}{5}x - 5 \). If you have a different line whose slope you want to test against, follow the same method!