Question

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)


y = –6x + 4


y = –8x – 8


y = 6x – 8


y = –6x – 4

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 need to follow these steps:

1. **Determine the slope of the given line.** The slope (m) of the line \( y = -6x + 2 \) is -6.

2. **Use the same slope for the parallel line.** Since parallel lines have the same slope, the slope of the 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 \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope.

Substituting \( m = -6 \) and the point \((-1, 2)\):

\[
y - 2 = -6(x + 1)
\]

4. **Simplify the equation:**

\[
y - 2 = -6x - 6
\]

\[
y = -6x - 4
\]

Thus, the equation of the line parallel to the given line and passing through the point \((-1, 2)\) is:

\[
\boxed{y = -6x - 4}
\]