Question

3.
Write an equation for the line that is parallel to the given line and that passes through the given point.

y = –6x + 2; (–1, 2)

Answer 1

To find the equation of a line that is parallel to the given line \( y = -6x + 2 \) and passes through the point \( (-1, 2) \), we can follow these steps:

1. **Determine the slope of the given line**: The slope-intercept form of the line is \( y = mx + b \), where \( m \) is the slope. In our case, the slope \( m \) of the given line is \( -6 \).

2. **Use the same slope for the parallel line**: Since parallel lines have the same slope, the slope of our new line will also be \( -6 \).

3. **Use the point-slope form of the equation of a line**: The point-slope form is given by \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) are the coordinates of the given point and \( m \) is the slope. Here, our point is \( (-1, 2) \) and our slope is \( -6 \).

Plugging the values into the point-slope form:
\[
y - 2 = -6(x - (-1))
\]
This simplifies to:
\[
y - 2 = -6(x + 1)
\]

4. **Distribute the slope**:
\[
y - 2 = -6x - 6
\]

5. **Add 2 to both sides to solve for \( y \)**:
\[
y = -6x - 6 + 2
\]
\[
y = -6x - 4
\]

So, the equation of the line that is parallel to the given line and passes through the point \( (-1, 2) \) is:
\[
\boxed{y = -6x - 4}
\]