What is the equation for the line perpendicular to the line represented by the equation y = x- 2 that passes through the point (4, –7)? O A. y =-3x – 2 о в. у3 -Зх- 5 O C. y = 3x + 2 о D. у3-3х + 5
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 18
![### Problem Statement
What is the equation for the line perpendicular to the line represented by the equation \(y = \frac{1}{3}x - 2\) that passes through the point \((4, -7)\)?
### Multiple Choice Options
- **A.** \(y = -3x - 2\)
- **B.** \(y = -3x - 5\)
- **C.** \(y = 3x + 2\)
- **D.** \(y = -3x + 5\)
### Explanation
To solve this problem, you need to:
1. Determine the slope of the given line.
2. Find the slope of the line perpendicular to the given line.
3. Use the point-slope form to find the equation of the perpendicular line that passes through the given point.
#### Step-by-Step Solution
1. **Identify the slope of the given line:**
The equation of the given line is \( y = \frac{1}{3}x - 2 \). The slope (\(m\)) is \(\frac{1}{3}\).
2. **Find the slope of the perpendicular line:**
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.
So, the slope \( m_{\text{perpendicular}} = -\frac{1}{(\frac{1}{3})} = -3 \).
3. **Use the point-slope form equation:**
The point-slope form of a line's equation is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \((x_1, y_1)\) is a point on the line. Here, \( m = -3 \) and the point is \( (4, -7) \).
Plug the slope and the point into the point-slope form:
\[
y - (-7) = -3(x - 4)
\]
Simplify:
\[
y + 7 = -3x + 12
\]
\[
y = -3x + 12 - 7
\]
\[
y = -3x + 5
\]
Therefore, the correct answer is:
- **D.** \(y = -3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc14456c8-c349-46c2-a794-2f6de4965e41%2F5a63c1d8-23b0-4059-8fcb-372c882588af%2Fr9q7jzp_processed.png&w=3840&q=75)
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