What is the equation in slope-intercept form of the line that passes through the point (2, −4)
 and is perpendicular to the line represented by y=23x+5
.
A.y=−32x+5

B.y=−32x−1

C.y=23x−4

D.y=23x+2


To solve this, we need to follow these steps:

1. **Identify the slope of the given line**: The given equation is \( y = \frac{2}{3}x + 5 \). Here, the slope \( m_1 = \frac{2}{3} \).

2. **Find the slope of the perpendicular line**: The slope of a line perpendicular to another is the negative reciprocal of the original slope. So, the slope of the line perpendicular to \( y = \frac{2}{3}x + 5 \) is \( m_2 = -\frac{3}{2} \).

3. **Use point-slope form to find the equation**: The point-slope form is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through. Substituting \( m = -\frac{3}{2} \) and the point \( (2, -4) \):
   \[
   y - (-4) = -\frac{3}{2}(x - 2)
   \]
   Simplifying this:
   \[
   y + 4 = -\frac{3}{2}(x - 2)
   \]
   \[
   y + 4 = -\frac{3}{2}x + 3
   \]
   \[
   y = -\frac{3}{2}x + 3 - 4
   \]
   \[
   y = -\frac{3}{2}x - 1
   \]

So, the equation of the line is \( y = -\frac{3}{2}x - 1 \).

### The correct answer is **B. \( y = -\frac{3}{2}x - 1 \)**.

Would you like any further details on how this works?

---

**Related Questions**:

1. What is the formula for the slope of a line perpendicular to another line?
2. How can you convert from point-slope form to slope-intercept form?
3. What happens if two lines have the same slope?
4. How do you find the equation of a line that passes through a given point?
5. Can a line be perpendicular to itself?

**Tip**: Remember that perpendicular lines have slopes that are negative reciprocals of each other!

What is the equation in slope-intercept form of the line that passes through the point (2, −4) and is perpendicular to the line represented by y = 2/3x + 5?

This solution shows how to find the equation of a line that passes through the point (2, -4) and is perpendicular to y = 2/3x + 5. Key concepts include perpendicular slopes and converting between point-slope and slope-intercept form. Perfect for students in Grades 8-10 learning about linear equations and geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation