What is the equation of the line that passes through the point (−4, −7)
 and is parallel to the line with equation y=2x+6
?
A.y=2x+1

B.y=2x−15

C.y=14x+6

D.y=134x+6


To find the equation of a line that passes through a given point and is parallel to another line, we follow these steps:

### Step 1: Identify the slope of the given line
The given equation of the line is \( y = 2x + 6 \). This is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope.

Thus, the slope \( m = 2 \).

### Step 2: Use the point-slope form
Since the lines are parallel, they have the same slope. Now, we'll use the point-slope form of the equation, which is:

\[
y - y_1 = m(x - x_1)
\]

where:
- \( m = 2 \) (slope of the parallel line),
- \( (x_1, y_1) = (-4, -7) \) (the given point).

Substitute these values into the equation:

\[
y - (-7) = 2(x - (-4))
\]

This simplifies to:

\[
y + 7 = 2(x + 4)
\]

### Step 3: Simplify the equation
Distribute the 2 on the right-hand side:

\[
y + 7 = 2x + 8
\]

Now, subtract 7 from both sides:

\[
y = 2x + 1
\]

### Conclusion:
The equation of the line is \( y = 2x + 1 \), which matches **option A**.

Would you like further details or clarification?

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Here are 5 related questions:

1. How do you determine the slope of a line from its equation?
2. What is the significance of parallel lines having the same slope?
3. How do you convert a point-slope form equation to slope-intercept form?
4. Can two lines be parallel if their slopes are different?
5. How can you find the y-intercept of a line passing through a given point?

**Tip:** For lines that are perpendicular, their slopes are negative reciprocals of each other!

What is the equation of the line that passes through the point (−4, −7) and is parallel to the line with equation y = 2x + 6?

Learn how to find the equation of a line that passes through the point (-4, -7) and is parallel to the line y = 2x + 6. This step-by-step solution covers key concepts such as slope-intercept form, point-slope form, and the properties of parallel lines. Suitable for students in Grades 8-10.

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