Write the equation of the line that is parallel to the given line described by the equation 6y=−12x−216y=−12x−21 and passes through the point (−4,9)(−4,9).

A.y=−12x+5y=−12x+5

B.y=−2x+7y=−2x+7

C.y=12x+11y=12x+11

D.y=12x+13y=12x+13


First, let's start by simplifying the given line's equation, \( 6y = -12x - 21 \).

### Step 1: Simplify the Given Equation
Divide both sides by 6 to isolate \( y \):
\[
y = -2x - 3.5
\]

This is in the slope-intercept form \( y = mx + b \), where \( m = -2 \). This means that the slope of the given line is \( -2 \).

### Step 2: Determine the Slope of the Parallel Line
Lines that are parallel have the same slope. Therefore, the line we are looking for must also have a slope of \( -2 \).

### Step 3: Use the Point-Slope Formula
We need to find the equation of the line that passes through the point \( (-4, 9) \) with a slope of \( -2 \). Using the point-slope formula \( y - y_1 = m(x - x_1) \), where \( m = -2 \) and \( (x_1, y_1) = (-4, 9) \):

\[
y - 9 = -2(x + 4)
\]

### Step 4: Simplify the Equation
Distribute \( -2 \) on the right side:
\[
y - 9 = -2x - 8
\]

Add 9 to both sides to solve for \( y \):
\[
y = -2x + 1
\]

### Final Answer
The equation of the line parallel to the given line and passing through \( (-4, 9) \) is:
\[
y = -2x + 1
\]

This matches none of the provided answer choices exactly, so the correct answer does not appear to be listed.

Would you like further clarification or have any questions about this solution? 

---

**Related Questions:**
1. What would be the equation of a line perpendicular to the original line and passing through the same point?
2. How do you derive the slope-intercept form from a standard form equation?
3. Can you explain why parallel lines have identical slopes?
4. How can the distance between two parallel lines be calculated?
5. What is the impact on the graph if the y-intercept of a line changes?

**Tip:** In problems involving parallel lines, the key is that they share identical slopes but can have different y-intercepts.

Write the equation of the line that is parallel to the given line described by the equation 6y = −12x − 21 and passes through the point (−4,9).

Discover how to determine the equation of a line parallel to 6y = −12x − 21 that passes through the point (−4,9). This step-by-step solution covers algebraic techniques for finding parallel lines and using the point-slope form. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation